diff options
| author | YanzhenXiang <54230111+YanzhenXiangRobotics@users.noreply.github.com> | 2023-11-06 16:49:26 +0100 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2023-11-06 16:49:26 +0100 |
| commit | d6b96c55ebb89ebd6e2d990ec89122799c68a230 (patch) | |
| tree | 7a837438da9e07a5e77658c6d882577fff8bcae1 | |
| parent | Update 23 (diff) | |
| parent | update the new submission zip generated from npross branch (diff) | |
| download | mpc_pe-d6b96c55ebb89ebd6e2d990ec89122799c68a230.tar.gz mpc_pe-d6b96c55ebb89ebd6e2d990ec89122799c68a230.zip | |
Submission
65 files changed, 9998 insertions, 35 deletions
@@ -1 +1,145 @@ -tbxmanager/
\ No newline at end of file +# npross +tags + +# Created by https://www.toptal.com/developers/gitignore/api/macos,linux,windows,matlab +# Edit at https://www.toptal.com/developers/gitignore?templates=macos,linux,windows,matlab + +### Linux ### +*~ + +# temporary files which can be created if a process still has a handle open of a deleted file +.fuse_hidden* + +# KDE directory preferences +.directory + +# Linux trash folder which might appear on any partition or disk +.Trash-* + +# .nfs files are created when an open file is removed but is still being accessed +.nfs* + +### macOS ### +# General +.DS_Store +.AppleDouble +.LSOverride + +# Icon must end with two \r +Icon + + +# Thumbnails +._* + +# Files that might appear in the root of a volume +.DocumentRevisions-V100 +.fseventsd +.Spotlight-V100 +.TemporaryItems +.Trashes +.VolumeIcon.icns +.com.apple.timemachine.donotpresent + +# Directories potentially created on remote AFP share +.AppleDB +.AppleDesktop +Network Trash Folder +Temporary Items +.apdisk + +### macOS Patch ### +# iCloud generated files +*.icloud + +### MATLAB ### +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +*.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Simulink cache files +*.slxc + +# Octave session info +octave-workspace + +### Windows ### +# Windows thumbnail cache files +Thumbs.db +Thumbs.db:encryptable +ehthumbs.db +ehthumbs_vista.db + +# Dump file +*.stackdump + +# Folder config file +[Dd]esktop.ini + +# Recycle Bin used on file shares +$RECYCLE.BIN/ + +# Windows Installer files +*.cab +*.msi +*.msix +*.msm +*.msp + +# Windows shortcuts +*.lnk + +# End of https://www.toptal.com/developers/gitignore/api/macos,linux,windows,matlab + +# Symbolic links +templates/TestFunction_generate_system_scaled.p +templates/TestFunction_MPC_TE_forces.p +templates/TestFunction.p +templates/TestFunction_lqr_maxPI.p +templates/TestFunction_compute_minRPI.p +templates/TestFunction_compute_tube_controller.p +templates/TestFunction_generate_params.p +templates/TestFunction_MPC_TS_SC.p +templates/TestFunction_MPC_TE.p +templates/TestFunction_MPC_TS.p +templates/TestFunction_compute_tightening.p +templates/run_tests.p +templates/TestFunction_lqr_tuning_script.p +templates/TestFunction_generate_system_cont.p +templates/TestFunction_traj_cost.p +templates/TestFunction_MPC.p +templates/TestFunction_traj_constraints.p +templates/TestFunction_simulate_uncertain.p +templates/TestFunction_lqr_tuning.p +templates/linearController.p +templates/TestFunction_simulate.p +templates/TestFunction_LQR.p +templates/TestFunction_generate_system.p +tbxmanager/ +templates/TestFunction_generate_constraints.p +templates/TestFunction_MPC_TUBE_script.p +templates/TestFunction_generate_disturbances.p +templates/TestFunction_MPC_TUBE.p +templates/TestFunction_MPC_TS_SC_script.p diff --git a/22956817_19150903_22943120.zip b/22956817_19150903_22943120.zip Binary files differnew file mode 100644 index 0000000..1e48ed3 --- /dev/null +++ b/22956817_19150903_22943120.zip diff --git a/MPC_TS_SC_params.mat b/MPC_TS_SC_params.mat Binary files differnew file mode 100644 index 0000000..2ff2f68 --- /dev/null +++ b/MPC_TS_SC_params.mat diff --git a/Submission files/LQR.m b/Submission files/LQR.m new file mode 100644 index 0000000..873546a --- /dev/null +++ b/Submission files/LQR.m @@ -0,0 +1,31 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef LQR + properties + K + end + + methods + %constructor + function obj = LQR(Q,R,params) + % YOUR CODE HERE + E = zeros(params.model.nx); + S = zeros(params.model.nx, params.model.nu); + Pinf = idare(params.model.A, params.model.B, Q, R); + obj.K = -inv(R + params.model.B' * Pinf * params.model.B) ... + * params.model.B' * Pinf * params.model.A; + end + + function [u, ctrl_info] = eval(obj,x) + % YOUR CODE HERE + u = obj.K * x; + ctrl_info = struct('ctrl_feas',true); + end + end +end diff --git a/Submission files/MPC.m b/Submission files/MPC.m new file mode 100644 index 0000000..355eb81 --- /dev/null +++ b/Submission files/MPC.m @@ -0,0 +1,71 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC + properties + yalmip_optimizer + end + + methods + function obj = MPC(Q,R,N,params) + nu = params.model.nu; + nx = params.model.nx; + % YOUR CODE HERE + A=params.model.A; + B=params.model.B; + U = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + X = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + + [K,P,~] = dlqr(A,B,Q,R); + +% s_max=params.constraints.MaxAbsPositionXZ; +% y_max=params.constraints.MaxAbsPositionY; +% u_max = params.constraints.MaxAbsThrust; + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; + X0 = sdpvar(nx,1,'full'); + objective = 0; + constraints = X{1} == X0; + for k = 1:N + constraints = [ ... + constraints, ... + X{k+1} == A*X{k} + B*U{k} , ... + H_x * X{k} <= h_x, ... + H_u * U{k} <= h_u ... + ]; + + objective = objective + X{k}'*Q*X{k} + U{k}'*R*U{k}; + end + objective=objective+X{N+1}'*P*X{N+1}; + % terminal constraint +% constraints = [ ... +% constraints, ... +% X{N+1} == zeros(nx,1) +% ]; + opts = sdpsettings('verbose',1,'solver','quadprog'); + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); + end + + function [u, ctrl_info] = eval(obj,x) + % evaluate control action by solving MPC problem + tic; + [optimizer_out,errorcode,~] = obj.yalmip_optimizer{x}; + solvetime = toc; + + [u, objective] = optimizer_out{:}; + + feasible = true; + if (errorcode ~= 0) + feasible = false; + end + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end diff --git a/Submission files/MPC_TE.m b/Submission files/MPC_TE.m new file mode 100644 index 0000000..747c7ee --- /dev/null +++ b/Submission files/MPC_TE.m @@ -0,0 +1,62 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC_TE + properties + yalmip_optimizer + end + + methods + function obj = MPC_TE(Q,R,N,params) + % YOUR CODE HERE + opts = sdpsettings('verbose',1,'solver','quadprog'); + + % Create yalmip variables + U = sdpvar(repmat(params.model.nu,N,1),ones(1,N)); + X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1)); + + % Build cost function and constraints + objective = 0; + constraints = []; + for k=1:N+1 + if k <= N + % These constraints are for the index in 1, ..., N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k}; + constraints = [constraints, ... + X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ... + params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ... + ]; + end + + % These contrains are for 1, ..., N+1 + constraints = [constraints, ... + params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ... + ]; + end + % Terminal constraint + constraints = [constraints, X{N+1} == zeros(size(X{N+1}))]; + + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective}); + end + + function [u, ctrl_info] = eval(obj,x) + %% evaluate control action by solving MPC problem, e.g. + tic; + [optimizer_out,errorcode] = obj.yalmip_optimizer(x); + solvetime = toc; + [u, objective] = optimizer_out{:}; + + feasible = true; + if (errorcode ~= 0) + feasible = false; + end + + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end
\ No newline at end of file diff --git a/Submission files/MPC_TE_forces.m b/Submission files/MPC_TE_forces.m new file mode 100644 index 0000000..5625f32 --- /dev/null +++ b/Submission files/MPC_TE_forces.m @@ -0,0 +1,38 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC_TE_forces + properties + forces_optimizer + end + + methods + function obj = MPC_TE_forces(Q,R,N,params) + % YOUR CODE HERE + opts = getOptions('forcesSolver'); + opts.printlevel = 0; + obj.forces_optimizer = % YOUR CODE HERE + end + + function [u, ctrl_info] = eval(obj,x) + %% evaluate control action by solving MPC problem, e.g. + [optimizer_out,errorcode,info] = obj.forces_optimizer(x); + u = optimizer_out; + objective = info.pobj; + solvetime = info.solvetime; + + feasible = true; + if any(errorcode ~= 1) + feasible = false; + warning('MPC infeasible'); + end + + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end
\ No newline at end of file diff --git a/Submission files/MPC_TS.m b/Submission files/MPC_TS.m new file mode 100644 index 0000000..cbe7b45 --- /dev/null +++ b/Submission files/MPC_TS.m @@ -0,0 +1,62 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC_TS + properties + yalmip_optimizer + end + + methods + function obj = MPC_TS(Q,R,N,H,h,params) + % YOUR CODE HERE + opts = sdpsettings('verbose',1,'solver','quadprog'); + + % Create yalmip optimization variables + U = sdpvar(repmat(params.model.nu,N,1),ones(1,N)); + X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1)); + + % Build cost function and constraints + Pinf = idare(params.model.A, params.model.B, Q, R); + objective = X{N+1}' * Pinf * X{N+1}; + constraints = []; + for k=1:N+1 + if k <= N + % These constraints are for the index in 1, ..., N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k}; + constraints = [constraints, ... + X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ... + params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ... + ]; + end + + % These contrains are for 1, ..., N+1 + constraints = [constraints, ... + params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ... + ]; + end + % Terminal constraint + constraints = [constraints, H*X{N+1} <= h]; + + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective}); end + + function [u, ctrl_info] = eval(obj,x) + %% evaluate control action by solving MPC problem, e.g. + tic; + [optimizer_out,errorcode] = obj.yalmip_optimizer(x); + solvetime = toc; + [u, objective] = optimizer_out{:}; + + feasible = true; + if (errorcode ~= 0) + feasible = false; + end + + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end
\ No newline at end of file diff --git a/Submission files/MPC_TS_SC.m b/Submission files/MPC_TS_SC.m new file mode 100644 index 0000000..fb1c720 --- /dev/null +++ b/Submission files/MPC_TS_SC.m @@ -0,0 +1,72 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC_TS_SC + properties + yalmip_optimizer + end + + methods + function obj = MPC_TS_SC(Q,R,N,H,h,S,v,params) + % YOUR CODE HERE + % initialize parameters + nu = params.model.nu; + nx = params.model.nx; + A=params.model.A; + B=params.model.B; + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; + [~,P,~] = dlqr(A,B,Q,R); + + U = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + X = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + sv = sdpvar(repmat(length(S(1,:)),1,N+1),ones(1,N+1),'full'); + + X0 = sdpvar(nx,1,'full'); + objective = 0; + constraints = X{1} == X0; + % items for 1 to N + for k=1:N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k} + sv{k}' * S * sv{k} + v * max(sv{k}); + constraints = [constraints, ... + X{k+1} == A * X{k} + B * U{k}, ... + H_x * X{k} <= h_x+sv{k}, ... + H_u * U{k} <= h_u, ... + sv{k} >= 0 ... + ]; + end + % items for N+1 + objective = objective + X{N+1}'*P*X{N+1} + sv{N+1}'*S*sv{N+1} + v*max(sv{N+1}); + constraints = [constraints, ... + sv{N+1} >= 0, ... + H_x * X{N+1} <= h_x + sv{N+1} ... + ]; + % maximum positively invariant set constraint + constraints = [constraints, H * X{N+1} <= h]; + opts = sdpsettings('verbose',1,'solver','quadprog','quadprog.TolFun',1e-8); + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); + end + + function [u, ctrl_info] = eval(obj,x) + % evaluate control action by solving MPC problem + tic; + [optimizer_out,errorcode,~] = obj.yalmip_optimizer{x}; + solvetime = toc; + + [u, objective] = optimizer_out{:}; + + feasible = true; + if (errorcode ~= 0) + feasible = false; + end + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end
\ No newline at end of file diff --git a/Submission files/MPC_TS_SC_script.m b/Submission files/MPC_TS_SC_script.m new file mode 100644 index 0000000..9499cf1 --- /dev/null +++ b/Submission files/MPC_TS_SC_script.m @@ -0,0 +1,14 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +S=100000000*eye(6); +v=100000000; +matfile=struct("S",S,"v",v); +save("MPC_TS_SC_params.mat","-struct","matfile") + + diff --git a/Submission files/MPC_TUBE.m b/Submission files/MPC_TUBE.m new file mode 100644 index 0000000..9a630c1 --- /dev/null +++ b/Submission files/MPC_TUBE.m @@ -0,0 +1,83 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +classdef MPC_TUBE + properties + yalmip_optimizer + K_tube + end + + methods + function obj = MPC_TUBE(Q,R,N,H_N,h_N,H_tube,h_tube,K_tube,params) + obj.K_tube = K_tube; + + % YOUR CODE HERE + nx = params.model.nx; + nu = params.model.nu; + + A = params.model.A; + B = params.model.B; + + [~,P,~] = dlqr(A,B,Q,R); + + V = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + Z = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; + + P_x_tightened = Polyhedron('A',H_x,'b',h_x).minus(Polyhedron('A',H_tube,'b',h_tube)); + H_z = P_x_tightened.A; + h_z = P_x_tightened.b; + + P_u_tightened = Polyhedron('A',H_u,'b',h_u).minus(K_tube*Polyhedron('A',H_tube,'b',h_tube)); + H_v = P_u_tightened.A; + h_v = P_u_tightened.b; + + X0 = sdpvar(nx,1,'full'); + constraints = [H_tube*(X0-Z{1}) <= h_tube]; + objective = 0; + for k = 1:N + constraints = [ ... + constraints, ... + Z{k+1} == A*Z{k} + B*V{k} , ... +% H_z * Z{k} <= h_z, ... +% H_v * V{k} <= h_v ... + H_x * Z{k} <= h_x, ... + H_u * V{k} <= h_u ... + ]; + objective = objective + Z{k}'*Q*Z{k} + V{k}'*R*V{k}; + end + constraints = [constraints, H_N * Z{end} <= h_N]; + objective = objective + Z{end}'*P*Z{end}; + + opts = sdpsettings('verbose',1,'solver','quadprog'); + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{V{1} Z{1} objective}); + end + + function [u, ctrl_info] = eval(obj,x) + %% evaluate control action by solving MPC problem, e.g. + tic; + [optimizer_out,errorcode] = obj.yalmip_optimizer(x); + solvetime = toc; + % YOUR CODE HERE + [v0, z0, objective] = optimizer_out{:}; + u = obj.K_tube*(x-z0)+v0; + + + feasible = true; + if (errorcode ~= 0) + feasible = false; + end + + ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); + end + end +end
\ No newline at end of file diff --git a/Submission files/MPC_TUBE_script.m b/Submission files/MPC_TUBE_script.m new file mode 100644 index 0000000..a021cd0 --- /dev/null +++ b/Submission files/MPC_TUBE_script.m @@ -0,0 +1,15 @@ +p = [0.05, 0.1]; +params = generate_params(); +params = generate_params_z(params); +K_tube = compute_tube_controller(p,params); +[H_tube, h_tube, n_iter] = compute_minRPI(K_tube, params); +params = compute_tightening(K_tube, H_tube, h_tube, params); + +Q = diag([300,0.1]);R = 1;N = 50; +[H_N, h_N] = lqr_maxPI(Q, R, params); + +% MPC_TUBE_obj = MPC_TUBE(Q,R,N,H_N,h_N,H_tube,h_tube,K_tube,params); +matfile = struct("p", p, "K_tube", K_tube, "H_tube", H_tube, "h_tube", h_tube,... + "H_N", H_N, "h_N", h_N, "params_z_tube", params); +save("MPC_TUBE_params.mat", "-struct", "matfile"); + diff --git a/Submission files/chebycenter.m b/Submission files/chebycenter.m new file mode 100644 index 0000000..cbdce1c --- /dev/null +++ b/Submission files/chebycenter.m @@ -0,0 +1,20 @@ +function [c,r] = chebycenter(A,b) +%CHEBYCENTER Compute Chebyshev center of polytope Ax <= b. +% The Chebyshev center of a polytope is the center of the largest +% hypersphere enclosed by the polytope. +% Requires optimization toolbox. + +[n,p] = size(A); +an = sqrt(sum(A.^2,2)); +A1 = zeros(n,p+1); +A1(:,1:p) = A; +A1(:,p+1) = an; +f = zeros(p+1,1); +f(p+1) = -1; + +options = optimset; +options = optimset(options,'Display', 'off'); +c = linprog(f,A1,b,[],[],[],[],[],options); +r = c(p+1); +c = c(1:p); +end diff --git a/Submission files/compute_minRPI.m b/Submission files/compute_minRPI.m new file mode 100644 index 0000000..19df517 --- /dev/null +++ b/Submission files/compute_minRPI.m @@ -0,0 +1,39 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [H_tube,h_tube,n_iter] = compute_minRPI(K_tube,params) + % YOUR CODE HERE + A = params.model.A+params.model.B*K_tube; + % A = params.model.A; +% display(A) + nx = params.model.nx; + omega = Polyhedron('A',[eye(nx);-eye(nx)],'b',zeros(1,2*nx)'); + % display(omega.A) + % display(omega.b) + n_iter = 0; + Hw = params.constraints.DisturbanceMatrix; + hw = params.constraints.DisturbanceRHS; + W = Polyhedron('A',Hw,'b',hw); + while true + omega_last = copy(omega); + % display(n_iter) + % A_last = omega.A; + % b_last = omega.b; + display(n_iter); + display(omega.b) + omega = omega.plus(A^(n_iter)*W); + + if eq(omega.minHRep(),omega_last.minHRep()) + % if eq(omega,omega_last) + break + end + n_iter = n_iter+1; + end + H_tube = omega.A; + h_tube = omega.b; +end
\ No newline at end of file diff --git a/Submission files/compute_tightening.m b/Submission files/compute_tightening.m new file mode 100644 index 0000000..7095f9c --- /dev/null +++ b/Submission files/compute_tightening.m @@ -0,0 +1,29 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function params = compute_tightening(K_tube,H_tube,h_tube,params) + % YOUR CODE HERE + Hx = params.constraints.StateMatrix; + hx = params.constraints.StateRHS; + + Hu = params.constraints.InputMatrix; + hu = params.constraints.InputRHS; + + Pxz = Polyhedron('A',Hx,'b',hx); + Puz = Polyhedron('A',Hu,'b',hu); + % Ptube = Polyhedron('A',H_tube,'b',h_tube); + + Px_tube = Pxz.minus(Polyhedron('A',H_tube,'b',h_tube)); + params.constraints.StateMatrix = Px_tube.A; + params.constraints.StateRHS = Px_tube.b; + + Pu_tube = Puz.minus(K_tube*Polyhedron('A',H_tube,'b',h_tube)) +% Pu_tube = Puz.minus(Polyhedron('A',H_tube*K_tube,'b',h_tube)); + params.constraints.InputMatrix = Pu_tube.A; + params.constraints.InputRHS = Pu_tube.b; +end
\ No newline at end of file diff --git a/Submission files/compute_tube_controller.m b/Submission files/compute_tube_controller.m new file mode 100644 index 0000000..2c567f0 --- /dev/null +++ b/Submission files/compute_tube_controller.m @@ -0,0 +1,16 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function K_tube = compute_tube_controller(p,params) + % YOUR CODE HERE + Az = params.model.A; + Bz =params.model.B; + % Bz = [params.model.B,eye(params.model.nx)]; + K_tube = -place(Az,Bz,p); + % K_tube = K(1:params.model.nu,:); +end
\ No newline at end of file diff --git a/Submission files/cprnd.m b/Submission files/cprnd.m new file mode 100644 index 0000000..4183ac3 --- /dev/null +++ b/Submission files/cprnd.m @@ -0,0 +1,296 @@ +function [X S] = cprnd(N,A,b,options) +%CPRND Draw from the uniform distribution over a convex polytope. +% X = cprnd(N,A,b) Returns an N-by-P matrix of random vectors drawn +% from the uniform distribution over the interior of the polytope +% defined by Ax <= b. A is a M-by-P matrix of constraint equation +% coefficients. b is a M-by-1 vector of constraint equation +% constants. +% +% cprnd(N,A,b,options) allows various options to be specified. + +% 'method' Specifies the algorithm. One of the strings 'gibbs', +% 'hitandrun' (the default), and 'achr'. The default +% algorithm 'hitandrun' is a vanilla hit-and-run sampler +% [1]. 'gibbs' specifies a Gibbs sampler, 'achr' is the +% Adaptive Centering Hit-and-Run algorithm of [2]. +% +% 'x0' Vector x0 is a starting point which should be interior +% to the polytope. If x0 is not supplied CPRND uses the +% Chebyshev center as the initial point. +% +% 'isotropic' Perform an adaptive istropic transformation of the +% polytope. The values 0, 1 and 2 respectively turn +% off the transformation, construct it during a runup +% period only, or continuously update the +% tranformation throughout sample production. The +% transformation makes sense only for the Gibbs and +% Hit-and-run samplers (ACHR is invariant under +% linear transformations). +% +% 'discard' Number of initial samples (post-runup) to discard. +% +% 'runup' When the method is gibbs or hitandrun and the +% isotropic transformation is used, this is the +% number of initial iterations of the algorithm in +% the untransformed space. That is a sample of size +% runup is generated and its covariance used as the +% basis of a transformation. +% When the method is achr runup is the number of +% conventional hitandrun iterations. See [2]. +% +% 'ortho' Zero/one flag. If turned on direction vectors for +% the hitandrun algorithm are generated in random +% orthonormal blocks rather than one by +% one. Experimental and of dubious utility. +% +% 'quasi' Allows the user to specify a quasirandom number generator +% (such as 'halton' or 'sobol'). Experimental and of +% dubious utility. +% +% + +% By default CPRND employs the hit-and-run sampler which may +% exhibit marked serial correlation and very long convergence times. +% +% References +% [1] Kroese, D.P. and Taimre, T. and Botev, Z.I., "Handbook of Monte +% Carlo Methods" (2011), pp. 240-244. +% [2] Kaufman, David E. and Smith, Robert L., "Direction Choice for +% Accelerated Convergence in Hit-and-Run Sampling", Op. Res. 46, +% pp. 84-95. +% +% Copyright (c) 2011-2012 Tim J. Benham, School of Mathematics and Physics, +% University of Queensland. + + function y = stdize(z) + y = z/norm(z); + end + + p = size(A,2); % dimension + m = size(A,1); % num constraint ineqs + x0 = []; + runup = []; % runup necessary to method + discard = []; % num initial pts discarded + quasi = 0; + method = 'achr'; + orthogonal = 0; + isotropic = []; + + % gendir generates a random unit (direction) vector. + gendir = @() stdize(randn(p,1)); + + % Alternative function ogendir forces directions to come in + % orthogonal bunches. + Ucache = {}; + function u = ogendir() + if length(Ucache) == 0 + u = stdize(randn(p,1)); + m = null(u'); % orthonormal basis for nullspace + Ucache = mat2cell(m',ones(1,p-1)); + else + u = Ucache{end}'; + Ucache(end) = []; + end + end + + % Check input arguments + + if m < p+1 + % obv a prob here + error('cprnd:obvprob',['At least ',num2str(p+1),' inequalities ' ... + 'required']); + end + + if nargin == 4 + if isstruct(options) + + if isfield(options,'method') + method = lower(options.method); + switch method + case 'gibbs' + case 'hitandrun' + case 'achr' + otherwise + error('cprnd:badopt',... + ['The method option takes only the ' ... + 'values "gibbs", "hitandrun", and "ACHR".']); + end + end + + if isfield(options,'isotropic') + % Controls application of isotropic transformation, + % which seems to help a lot. + isotropic = options.isotropic; + end + + if isfield(options,'discard') + % num. of samples to discard + discard = options.discard; + end + + if isfield(options,'quasi') + % Use quasi random numbers, which doesn't seem to + % help much. + quasi = options.quasi; + if quasi && ~ischar(quasi), quasi='halton'; end + if ~strcmp(quasi,'none') + qstr = qrandstream(quasi,p,'Skip',1); + gendir = @() stdize(norminv(qrand(qstr,1),0,1)'); + end + end + + if isfield(options,'x0') + % initial interior point + x0 = options.x0; + end + + if isfield(options,'runup') + % number of points to generate before first output point + runup = options.runup; + end + + if isfield(options,'ortho') + % Generate direction vectors in orthogonal + % groups. Seems to help a little. + orthogonal = options.ortho; + end + + else + x0 = options; % legacy support + end + end + + % Default and apply options + + if isempty(isotropic) + if ~strcmp(method,'achr') + isotropic = 2; + else + isotropic = 0; + end + end + + if orthogonal + gendir = @() ogendir(); + end + + % Choose a starting point x0 if user did not provide one. + if isempty(x0) + x0 = chebycenter(A,b); % prob. if p==1? + end + + % Default the runup to something arbitrary. + if isempty(runup) + if strcmp(method,'achr') + runup = 10*(p+1); + elseif isotropic > 0 + runup = 10*p*(p+1); + else + runup = 0; + end + end + + % Default the discard to something arbitrary + if isempty(discard) + if strcmp(method,'achr') + discard = 25*(p+1); + else + discard = runup; + end + end + + X = zeros(N+runup+discard,p); + + n = 0; % num generated so far + x = x0; + + % Initialize variables for keeping track of sample mean, covariance + % and isotropic transform. + M = zeros(p,1); % Incremental mean. + S2 = zeros(p,p); % Incremental sum of + % outer prodcts. + S = eye(p); T = eye(p); W = A; + + while n < N+runup+discard + y = x; + + % compute approximate stochastic transformation + if isotropic>0 + if n == runup || (isotropic > 1 && n > runup) + T = chol(S,'lower'); + W = A*T; + end + y = T\y; + end + + switch method + + case 'gibbs' + % choose p new components + for i = 1:p + % Find points where the line with the (p-1) components x_i + % fixed intersects the bounding polytope. + e = circshift(eye(p,1),i-1); + z = W*e; + c = (b - W*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % choose a point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*e; + end + + case 'hitandrun' + % choose a direction + u = gendir(); + % determine intersections of x + ut with the polytope + z = W*u; + c = (b - W*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % choose a point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*u; + + case 'achr' + % test whether in runup or not + if n < runup + % same as hitandrun + u = gendir(); + else + % choose a previous point at random + v = X(randi(n),:)'; + % line sampling direction is from v to sample mean + u = (v-M)/norm(v-M); + end + % proceed as in hit and run + z = A*u; + c = (b - A*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % Choose a random point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*u; + end + + if isotropic>0 + x = T*y; + else + x = y; + end + + X(n+1,:)=x'; + n = n + 1; + + % Incremental mean and covariance updates + delta0 = x - M; % delta new point wrt old mean + M = M + delta0/n; % sample mean + delta1 = x - M; % delta new point wrt new mean + if n > 1 + S2 = S2 + (n-1)/(n*n)*delta0*delta0'... + + delta1*delta1'; + S0 = S; + S = S2/(n-1); % sample covariance + else + S = eye(p); + end + + end + + X = X((discard+runup+1):(N+discard+runup),:); + +end diff --git a/Submission files/declaration-originality.pdf b/Submission files/declaration-originality.pdf new file mode 100644 index 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\ No newline at end of file diff --git a/Submission files/generate_disturbances.m b/Submission files/generate_disturbances.m new file mode 100644 index 0000000..f08cdb5 --- /dev/null +++ b/Submission files/generate_disturbances.m @@ -0,0 +1,17 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function Wt = generate_disturbances(params) + % YOUR CODE HERE + % params_z = generate_params_z(params); + Hw = params.constraints.DisturbanceMatrix; + hw = params.constraints.DisturbanceRHS; + % Pw = Polyhedron('A', Hw, 'b', hw); + N = params.model.HorizonLength; + Wt = cprnd(N,Hw,hw)'; +end
\ No newline at end of file diff --git a/Submission files/generate_params.m b/Submission files/generate_params.m new file mode 100644 index 0000000..4b61e31 --- /dev/null +++ b/Submission files/generate_params.m @@ -0,0 +1,58 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [params] = generate_params() +params = struct(); + +Tf = 60*60*24 * 2; % = 2 days +dt = 60 * 10; % = 10 minutes + +% model +params.model = struct(... + 'nx', 6, ... + 'nu', 3, ... + 'Mass', 300, ... + 'GravitationalParameter', 3.986e14, ... + 'ScalingMatrix', [1e-6*eye(3), zeros(3); zeros(3), 1e-3*eye(3)], ... + 'TargetRadius', 7000e3, ... + 'TimeStep', dt, ... + 'HorizonLength', ceil(Tf / dt), ... + 'InitialConditionA', [-15e-3; -400e-3; 24.4e-3; 0; 0.0081; 0], ... + 'InitialConditionB', [-20e-3; 400e-3; 24.4e-3; 0; 0.0108; 0], ... + 'InitialConditionC', [0.02; 0.01; -0.005; 0; 0; 0] ... +); + +% constraints +params.constraints = struct(... + 'MaxAbsPositionXZ', 0.1, ... + 'MaxAbsPositionY', 1, ... + 'MaxAbsThrust', 1, ... + 'MaxFinalPosDiff' , 3e-4, ... + 'MaxFinalVelDiff', 1e-3 ... +); + +params.exercise = struct( ... + 'QdiagOptA', [94.0; 0.1579; 300; 0.01; 0.10; 0.10] ... +); + +% Add system model +[Ac, Bc] = generate_system_cont(params); +[At, Bt] = generate_system(Ac, Bc, params); +[A, B] = generate_system_scaled(At, Bt, params); + +params.model.A = A; +params.model.B = B; + +% Add constraints +[H_u, h_u, H_x, h_x] = generate_constraints(params); +params.constraints.InputMatrix = H_u; +params.constraints.InputRHS = h_u; +params.constraints.StateMatrix = H_x; +params.constraints.StateRHS = h_x; + +end diff --git a/Submission files/generate_params_z.m b/Submission files/generate_params_z.m new file mode 100644 index 0000000..a7cfaa9 --- /dev/null +++ b/Submission files/generate_params_z.m @@ -0,0 +1,55 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [params_z] = generate_params_z(params) +% initialize params_z +params_z = params; + +% add initial condition of z-subsystem +params_z.model = rmfield(params_z.model,{'InitialConditionA', ... + 'InitialConditionB', ... + 'InitialConditionC'}); +params_z.model.InitialConditionA_z = [-0.07;0.04]; % TODO: tune + +% define projection matrices +T_z_x = [0 0 1 0 0 0; + 0 0 0 0 0 1]; +T_z_u = [0 0 1]; + +% projected system dynamics +params_z.model.A = T_z_x*params.model.A*T_z_x'; +params_z.model.B = T_z_x*params.model.B*T_z_u'; +params_z.model.nx = 2; +params_z.model.nu = 1; + +% state constraints +Hx = params.constraints.StateMatrix * T_z_x'; +hx = params.constraints.StateRHS; +X = Polyhedron('A',Hx,'b',hx); +X.minHRep(); + +params_z.constraints.StateMatrix = X.A; +params_z.constraints.StateRHS = X.b; + +% input constraints +Hu = params.constraints.InputMatrix * T_z_u'; +hu = params.constraints.InputRHS; +U = Polyhedron('A',Hu,'b',hu); + +params_z.constraints.InputMatrix = U.A; +params_z.constraints.InputRHS = U.b; + +% disturbance constraints +max_disturbance = 1e-4; % TODO: chose +params_z.constraints.MaxAbsDisturbance = max_disturbance; +H_w = kron(eye(params_z.model.nx),[1;-1]); +h_w = ones(2*params_z.model.nx, 1) * max_disturbance; + +params_z.constraints.DisturbanceMatrix = H_w; +params_z.constraints.DisturbanceRHS = h_w; +end diff --git a/Submission files/generate_system.m b/Submission files/generate_system.m new file mode 100644 index 0000000..b44bef2 --- /dev/null +++ b/Submission files/generate_system.m @@ -0,0 +1,15 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [A, B] = generate_system(Ac, Bc, params) + sys = ss(Ac, Bc, eye(params.model.nx), zeros(params.model.nx, params.model.nu)); + sysd = c2d(sys, params.model.TimeStep); + + A = sysd.A; + B = sysd.B; +end diff --git a/Submission files/generate_system_cont.m b/Submission files/generate_system_cont.m new file mode 100644 index 0000000..048ee7b --- /dev/null +++ b/Submission files/generate_system_cont.m @@ -0,0 +1,22 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [Ac, Bc] = generate_system_cont(params) + % YOUR CODE HERE + omega_n_sq = params.model.GravitationalParameter / params.model.TargetRadius^3; + omega_n = sqrt(omega_n_sq); + + Ac = [ + zeros(3), eye(3); + 3*omega_n_sq, 0, 0, 0, 2*omega_n, 0; + 0, 0, 0, -2*omega_n, 0, 0; + 0, 0, -omega_n_sq, 0, 0, 0; + ]; + + Bc = [zeros(3); eye(3);] / params.model.Mass; +end diff --git a/Submission files/generate_system_scaled.m b/Submission files/generate_system_scaled.m new file mode 100644 index 0000000..d65c7b3 --- /dev/null +++ b/Submission files/generate_system_scaled.m @@ -0,0 +1,16 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [A, B] = generate_system_scaled(At, Bt, params) + % YOUR CODE HERE + V = params.model.ScalingMatrix; + Vinv = inv(V); + + A = V*At*Vinv; + B = V*Bt; +end diff --git a/Submission files/lqr_maxPI.m b/Submission files/lqr_maxPI.m new file mode 100644 index 0000000..99b5b22 --- /dev/null +++ b/Submission files/lqr_maxPI.m @@ -0,0 +1,45 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +function [H, h] = lqr_maxPI(Q, R, params) + % Define the linear system + A = params.model.A; + B = params.model.B; + nx=params.model.nx; + nu=params.model.nu; + + s_max= params.constraints.MaxAbsPositionXZ; + y_max= params.constraints.MaxAbsPositionY; + u_max = params.constraints.MaxAbsThrust; + + K = -dlqr(A, B, Q, R); + systemLQR = LTISystem('A', A+B*K); +% absxmax = ones(nx,1)*s_max; +% absumax = ones(nu,1)*u_max; +% Xp = Polyhedron('A',[eye(nx); -eye(nx); K; -K], 'b', [absxmax;absxmax; absumax;absumax]); + Hx=params.constraints.StateMatrix; + hx=params.constraints.StateRHS; + Hu=params.constraints.InputMatrix; + hu=params.constraints.InputRHS; + Xp = Polyhedron('A',[Hx;Hu*K], 'b', [hx;hu]); + + figure(1); + systemLQR.x.with('setConstraint'); + systemLQR.x.setConstraint = Xp; + InvSetLQR = systemLQR.invariantSet(); +% InvSetLQR.plot(), alpha(0.25), title('Invariant Set for Triple Integrator under LQR Control'), xlabel('x_1'), ylabel('x_2'), zlabel('x_3'); + + H=InvSetLQR.A; + h=InvSetLQR.b; + + +end + + + diff --git a/Submission files/lqr_tuning.m b/Submission files/lqr_tuning.m new file mode 100644 index 0000000..9c9aab9 --- /dev/null +++ b/Submission files/lqr_tuning.m @@ -0,0 +1,55 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [tuning_struct, i_opt] = lqr_tuning(x0,Q,params) + % YOUR CODE HERE + i_opt = nan; + best_J_u = inf; + + % Prepare an array of empty structs + tuning_struct = repmat(struct( ... + 'InitialCondition', {}, ... + 'Qdiag', {}, ... + 'MaxAbsPositionXZ', {}, ... + 'MaxAbsPositionY', {}, ... + 'MaxAbsThrust', {}, ... + 'InputCost', {}, ... + 'MaxFinalPosDiff', {}, ... + 'MaxFinalVelDiff', {}, ... + 'TrajFeasible', {} ... + ), size(Q,2), 1); + + for i=1:size(Q,2) + tuning_struct(i).InitialCondition = x0; + tuning_struct(i).Qdiag = Q(:,i); + + ctrl = LQR(diag(Q(:,i)), eye(params.model.nu), params); + [Xt, Ut, ~] = simulate(x0, ctrl, params); + + [s_max, y_max, u_max, J_u, df_max, vf_max, traj_feas] = ... + traj_constraints(Xt, Ut, params); + + tuning_struct(i).MaxAbsPositionXZ = s_max; + tuning_struct(i).MaxAbsPositionY = y_max; + tuning_struct(i).MaxAbsThrust = u_max; + tuning_struct(i).InputCost = J_u; + tuning_struct(i).MaxFinalPosDiff = df_max; + tuning_struct(i).MaxFinalVelDiff = vf_max; + tuning_struct(i).TrajFeasible = traj_feas; + + if traj_feas + if J_u < best_J_u + i_opt = i; + best_J_u = J_u; + end + end + end + + % because the test suite wants a column vector + tuning_struct = tuning_struct'; +end diff --git a/Submission files/lqr_tuning_script.m b/Submission files/lqr_tuning_script.m new file mode 100644 index 0000000..4a02fc6 --- /dev/null +++ b/Submission files/lqr_tuning_script.m @@ -0,0 +1,58 @@ +function [tuning_struct] = lqr_tuning_script(params) + % From the hint: look in the vicinity of vector from the next section + % also from the hint: qx, qy, qvx, qvy are decoupled from qz, qvz + q_start = [94, .1579, 300, .01, .1, .1]; + + % parameters for sampling + v = 0.4; % search around q +- v * q + nsamples = 3; + + q = q_start; + best_J_u = inf; + while best_J_u > 7.6 + % Create sampling grid + range = linspace(1-v, 1+v, nsamples)'; + + % Sample in qx qy qvx qvy + G = kron(q([1,2,4,5]), range); + [Sx, Sy, Svx, Svy] = ndgrid(G(:,1), G(:,2), G(:,3), G(:,4)); + Q = [Sx(:), Sy(:), q(3) * ones(size(Sx(:))), ... + Svx(:), Svy(:), q(6) * ones(size(Sx(:)))]'; + + % Find best q + [ts, i_opt] = lqr_tuning(params.model.InitialConditionA, Q, params); + + % Save new best solution + if ~ isnan(i_opt) + tuning_struct = ts(i_opt); + best_J_u = ts(i_opt).InputCost; + q = ts(i_opt).Qdiag'; + end + + % Sample in qz qvz + G = kron(q([3,6]), range); + [Sz, Svz] = ndgrid(G(:,1), G(:,2)); + qs = kron(q, ones(size(Sz(:)))); + Q = [qs(:,1:2), Sz(:), qs(:,3:4), Svz(:)]'; + + % Find best item + [ts, i_opt] = lqr_tuning(params.model.InitialConditionA, Q, params); + + % Save new best solution + if ~ isnan(i_opt) + tuning_struct = ts(i_opt); + best_J_u = ts(i_opt).InputCost; + q = ts(i_opt).Qdiag'; + end + + % Search in a narrower region, increase resolution + v = v / 2; + + % Log + fprintf("Lowest J_u so far: %d, searching with v=%f\n", best_J_u,v); + end + + % Save for test + matfile = struct("tuning_struct", tuning_struct, "q", tuning_struct.Qdiag); + save("lqr_tuning_script.mat", "-struct", "matfile"); +end diff --git a/Submission files/plot_trajectory.m b/Submission files/plot_trajectory.m new file mode 100644 index 0000000..9bcb696 --- /dev/null +++ b/Submission files/plot_trajectory.m @@ -0,0 +1,126 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [fig_time,axes_time,fig_pos,axes_pos] = plot_trajectory(x,u,ctrl_info,params) + fig_time = figure; + + % check if input is 3-dimensional + n_traj = size(x,3); + assert(size(u,3) == n_traj); + assert(size(ctrl_info,3) == n_traj); + + nx = params.model.nx; + assert(nx == size(x,1)); + + t = 0:params.model.TimeStep:params.model.TimeStep*params.model.HorizonLength; + + % plot + axes_time = cell(5,1); + axes_time{1} = subplot(5,1,1); + hold on; + + for i = 1:n_traj + plot(axes_time{1},t,x(1,:,i),'DisplayName',sprintf('x_%d',i)); + plot(axes_time{1},t,x(3,:,i),'DisplayName',sprintf('z_%d',i)); + end + legend('Location','EastOutside') + + % max position + x_max = params.constraints.MaxAbsPositionXZ; + plot(axes_time{1}, [t(1); t(end)],[x_max; x_max],'k--','HandleVisibility','off'); + plot(axes_time{1}, [t(1); t(end)],[-x_max; -x_max],'k--','HandleVisibility','off'); + ylabel('Position [Mm]') + + axes_time{2} = subplot(5,1,2); + hold on; + for i = 1:n_traj + plot(axes_time{2},t,x(2,:,i),'DisplayName',sprintf('y_%d',i)); + end + + % max position + y_max = params.constraints.MaxAbsPositionY; + plot(axes_time{2},[t(1); t(end)],[y_max; y_max],'k--','HandleVisibility','off'); + plot(axes_time{2},[t(1); t(end)],[-y_max; -y_max],'k--','HandleVisibility','off'); + + legend('Location','EastOutside') + ylabel('Position [Mm]') + + axes_time{3} = subplot(5,1,3); + hold on; + for i = 1:n_traj + plot(axes_time{3},t,x(4,:,i),'DisplayName',sprintf('v_{x%d}',i)); + plot(axes_time{3},t,x(5,:,i),'DisplayName',sprintf('v_{y%d}',i)); + plot(axes_time{3},t,x(6,:,i),'DisplayName',sprintf('v_{z%d}',i)); + end + + legend('Location','EastOutside') + ylabel('Velocity [km/s]') + + axes_time{4} = subplot(5,1,4); + hold on; + % append one input value for plotting + u(:,length(t),:) = u(:,length(t)-1,:); + for i = 1:n_traj + stairs(axes_time{4},t,u(1,:,i)','DisplayName',sprintf('u_{x%d}',i)); + stairs(axes_time{4},t,u(2,:,i)','DisplayName',sprintf('u_{y%d}',i)); + stairs(axes_time{4},t,u(3,:,i)','DisplayName',sprintf('u_{z%d}',i)); + end + + % max thrust + thrust_max = params.constraints.MaxAbsThrust; + plot([t(1); t(end)],[thrust_max; thrust_max],'k--','HandleVisibility','off'); + plot([t(1); t(end)],[-thrust_max; -thrust_max],'k--','HandleVisibility','off'); + legend('Location','EastOutside') + ylabel('Thrust [N]') + + % feasibility + axes_time{5} = subplot(5,1,5); + hold on; + for i = 1:n_traj + % append one input value for plotting + ctrl_feas = [ctrl_info(:,:,i).ctrl_feas]; + ctrl_feas(length(t)) = ctrl_feas(length(t) - 1); + stairs(axes_time{5},t,ctrl_feas','DisplayName',sprintf('feas_%d',i)); + end + legend('Location','EastOutside') + ylabel('Controller feasible [0/1]') + + % link axes + axes_time = [axes_time{:}]; + linkaxes(axes_time,'x'); + xlabel('Time [s]') + + % plot without time + % YX-plane + fig_pos = figure; + axes_pos = cell(2,1); + axes_pos{1} = subplot(2,1,1); + hold on + colormap('hsv') + + for i = 1:n_traj + plot(axes_pos{1},x(2,:,i),x(1,:,i)); + end + + axis equal + xlabel('Y-Position [m]') + ylabel('X-Position [Mm]') + + % YZ plane + axes_pos{2} = subplot(2,1,2); + hold on + for i = 1:n_traj + plot(axes_pos{2},x(2,:,i),x(3,:,i)) + end + axis equal + xlabel('Y-Position [Mm]') + ylabel('Z-Position [Mm]') + + axes_pos = [axes_pos{:}]; + linkaxes(axes_pos,'x'); +end
\ No newline at end of file diff --git a/Submission files/plot_trajectory_z.m b/Submission files/plot_trajectory_z.m new file mode 100644 index 0000000..1b5a842 --- /dev/null +++ b/Submission files/plot_trajectory_z.m @@ -0,0 +1,78 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +function [fig_time,axes_time,fig_pos,axes_pos] = plot_trajectory_z(x,u,ctrl_info,params) + fig_time = figure; + + % check if input is 3-dimensional + n_traj = size(x,3); + assert(size(u,3) == n_traj); + assert(size(ctrl_info,3) == n_traj); + + nx = params.model.nx; + assert(nx == size(x,1)); + + t = 0:params.model.TimeStep:params.model.TimeStep*params.model.HorizonLength; + + % plot + axes_time = cell(4,1); + axes_time{1} = subplot(4,1,1); + hold on; + + for i = 1:n_traj + plot(axes_time{1},t,x(1,:,i),'DisplayName',sprintf('z_%d',i)); + end + legend('Location','EastOutside') + + % max position + x_max = params.constraints.MaxAbsPositionXZ; %*T(1); + plot(axes_time{1}, [t(1); t(end)],[x_max; x_max],'k--','HandleVisibility','off'); + plot(axes_time{1}, [t(1); t(end)],[-x_max; -x_max],'k--','HandleVisibility','off'); + ylabel('Position [Mm]') + + axes_time{2} = subplot(4,1,2); + hold on; + for i = 1:n_traj + plot(axes_time{2},t,x(2,:,i),'DisplayName',sprintf('v_{z%d}',i)); + end + legend('Location','EastOutside') + ylabel('Velocity [km/s]') + + axes_time{3} = subplot(4,1,3); + hold on; + % append one input value for plotting + u(:,length(t),:) = u(:,length(t)-1,:); + for i = 1:n_traj + stairs(axes_time{3},t,u(1,:,i)','DisplayName',sprintf('u_{z%d}',i)); + end + + % max thrust + thrust_max = params.constraints.MaxAbsThrust; + plot([t(1); t(end)],[thrust_max; thrust_max],'k--','HandleVisibility','off'); + plot([t(1); t(end)],[-thrust_max; -thrust_max],'k--','HandleVisibility','off'); + legend('Location','EastOutside') + ylabel('Thrust [N]') + + % feasibility + axes_time{4} = subplot(4,1,4); + hold on; + for i = 1:n_traj + % append one input value for plotting + ctrl_feas = [ctrl_info(:,:,i).ctrl_feas]; + ctrl_feas(length(t)) = ctrl_feas(length(t) - 1); + stairs(axes_time{4},t,ctrl_feas','DisplayName',sprintf('feas_%d',i)); + end + legend('Location','EastOutside') + ylabel('Feasible [0/1]') + + % link axes + axes_time = [axes_time{:}]; + linkaxes(axes_time,'x') + xlabel('Time [s]') +end
\ No newline at end of file diff --git a/Submission files/simulate.m b/Submission files/simulate.m new file mode 100644 index 0000000..6be40c3 --- /dev/null +++ b/Submission files/simulate.m @@ -0,0 +1,23 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [Xt,Ut,ctrl_info] = simulate(x0, ctrl, params) + % YOUR CODE HERE + % Hint: you can access the control command with ctrl.eval(x(:,i)) + + Xt = zeros(params.model.nx, params.model.HorizonLength+1); + Ut = zeros(params.model.nu, params.model.HorizonLength); + ctrl_info = repmat(struct('ctrl_feas',true), 1, params.model.HorizonLength); + + Xt(:,1) = x0; + for k=1:params.model.HorizonLength + [u, ~] = ctrl.eval(Xt(:,k)); + Ut(:,k) = u; + Xt(:,k+1) = params.model.A * Xt(:,k) + params.model.B * Ut(:,k); + end +end diff --git a/Submission files/simulate_uncertain.m b/Submission files/simulate_uncertain.m new file mode 100644 index 0000000..f74f7af --- /dev/null +++ b/Submission files/simulate_uncertain.m @@ -0,0 +1,24 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [Xt,Ut,ctrl_info] = simulate_uncertain(x0, ctrl, Wt, params) + % YOUR CODE HERE + Xt = [x0]; + Ut = []; + x = x0 + ctrl_info = []; + % obj = LQR(); + for i = 1:params.model.HorizonLength + [u, ctrl_info_] = ctrl.eval(x); + Ut = [Ut u]; + ctrl_info = [ctrl_info ctrl_info_]; + x = params.model.A*x + params.model.B*u + Wt(:,i); + Xt = [Xt x]; + end + % plot_trajectory(Xt, Ut, ctrl_info, params); +end
\ No newline at end of file diff --git a/Submission files/test_struct.mat b/Submission files/test_struct.mat Binary files differnew file mode 100644 index 0000000..14d32f6 --- /dev/null +++ b/Submission files/test_struct.mat diff --git a/Submission files/traj_constraints.m b/Submission files/traj_constraints.m new file mode 100644 index 0000000..69d19d3 --- /dev/null +++ b/Submission files/traj_constraints.m @@ -0,0 +1,40 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [s_max, y_max, u_max, J_u, df_max, vf_max, traj_feas] = traj_constraints(x,u,params) + % YOUR CODE HERE + + s_max = max(max(abs(x([1,3],:)))); + y_max = max(abs(x(2,:))); + u_max = max(max(abs(u))); + + J_u = 0; + for k=1:size(u,2) + J_u = J_u + u(:,k)' * u(:,k); + end + + df_max = sqrt(sum(x(1:3,end).^2)); + vf_max = sqrt(sum(x(4:6,end).^2)); + + constr = [ + s_max <= params.constraints.MaxAbsPositionXZ, ... + y_max <= params.constraints.MaxAbsPositionY, ... + u_max <= params.constraints.MaxAbsThrust, ... + df_max <= params.constraints.MaxFinalPosDiff, ... + vf_max <= params.constraints.MaxFinalVelDiff + ]; + + % disp([s_max, y_max, df_max, vf_max]) + % disp([params.constraints.MaxAbsPositionXZ, ... + % params.constraints.MaxAbsPositionY, ... + % params.constraints.MaxFinalPosDiff, ... + % params.constraints.MaxFinalVelDiff]) + % disp(constr') + traj_feas = all(constr); +end + diff --git a/Submission files/traj_cost.m b/Submission files/traj_cost.m new file mode 100644 index 0000000..57566c9 --- /dev/null +++ b/Submission files/traj_cost.m @@ -0,0 +1,17 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function J_Nt = traj_cost(Xt,Ut,Q,R) + % YOUR CODE HERE + J_Nt=0; + for i=1:length(Xt(1,:))-1 + a= Xt(:,i)'*Q*Xt(:,i); + b= Ut(:,i)'*R*Ut(:,i); + J_Nt=J_Nt+a+b; + end +end
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\ No newline at end of file +end diff --git a/templates/MPC.m b/templates/MPC.m index 3e9d2f1..355eb81 100644 --- a/templates/MPC.m +++ b/templates/MPC.m @@ -15,31 +15,57 @@ classdef MPC function obj = MPC(Q,R,N,params) nu = params.model.nu; nx = params.model.nx; - - % define optimization variables + % YOUR CODE HERE + A=params.model.A; + B=params.model.B; U = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + X = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + + [K,P,~] = dlqr(A,B,Q,R); + +% s_max=params.constraints.MaxAbsPositionXZ; +% y_max=params.constraints.MaxAbsPositionY; +% u_max = params.constraints.MaxAbsThrust; + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; X0 = sdpvar(nx,1,'full'); + objective = 0; + constraints = X{1} == X0; + for k = 1:N + constraints = [ ... + constraints, ... + X{k+1} == A*X{k} + B*U{k} , ... + H_x * X{k} <= h_x, ... + H_u * U{k} <= h_u ... + ]; - % YOUR CODE HERE - + objective = objective + X{k}'*Q*X{k} + U{k}'*R*U{k}; + end + objective=objective+X{N+1}'*P*X{N+1}; + % terminal constraint +% constraints = [ ... +% constraints, ... +% X{N+1} == zeros(nx,1) +% ]; opts = sdpsettings('verbose',1,'solver','quadprog'); obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); end function [u, ctrl_info] = eval(obj,x) - %% evaluate control action by solving MPC problem, e.g. + % evaluate control action by solving MPC problem tic; - [optimizer_out,errorcode] = obj.yalmip_optimizer(x); + [optimizer_out,errorcode,~] = obj.yalmip_optimizer{x}; solvetime = toc; - + [u, objective] = optimizer_out{:}; feasible = true; if (errorcode ~= 0) feasible = false; end - ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); end end -end
\ No newline at end of file +end diff --git a/templates/MPC_TE.m b/templates/MPC_TE.m index e0b55d2..747c7ee 100644 --- a/templates/MPC_TE.m +++ b/templates/MPC_TE.m @@ -15,7 +15,33 @@ classdef MPC_TE function obj = MPC_TE(Q,R,N,params) % YOUR CODE HERE opts = sdpsettings('verbose',1,'solver','quadprog'); - obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); + + % Create yalmip variables + U = sdpvar(repmat(params.model.nu,N,1),ones(1,N)); + X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1)); + + % Build cost function and constraints + objective = 0; + constraints = []; + for k=1:N+1 + if k <= N + % These constraints are for the index in 1, ..., N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k}; + constraints = [constraints, ... + X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ... + params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ... + ]; + end + + % These contrains are for 1, ..., N+1 + constraints = [constraints, ... + params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ... + ]; + end + % Terminal constraint + constraints = [constraints, X{N+1} == zeros(size(X{N+1}))]; + + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective}); end function [u, ctrl_info] = eval(obj,x) diff --git a/templates/MPC_TS.m b/templates/MPC_TS.m index 05f92ff..cbe7b45 100644 --- a/templates/MPC_TS.m +++ b/templates/MPC_TS.m @@ -15,8 +15,34 @@ classdef MPC_TS function obj = MPC_TS(Q,R,N,H,h,params) % YOUR CODE HERE opts = sdpsettings('verbose',1,'solver','quadprog'); - obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); - end + + % Create yalmip optimization variables + U = sdpvar(repmat(params.model.nu,N,1),ones(1,N)); + X = sdpvar(repmat(params.model.nx,N+1,1),ones(1,N+1)); + + % Build cost function and constraints + Pinf = idare(params.model.A, params.model.B, Q, R); + objective = X{N+1}' * Pinf * X{N+1}; + constraints = []; + for k=1:N+1 + if k <= N + % These constraints are for the index in 1, ..., N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k}; + constraints = [constraints, ... + X{k+1} == params.model.A * X{k} + params.model.B * U{k}, ... + params.constraints.InputMatrix * U{k} <= params.constraints.InputRHS, ... + ]; + end + + % These contrains are for 1, ..., N+1 + constraints = [constraints, ... + params.constraints.StateMatrix * X{k} <= params.constraints.StateRHS, ... + ]; + end + % Terminal constraint + constraints = [constraints, H*X{N+1} <= h]; + + obj.yalmip_optimizer = optimizer(constraints,objective,opts,X{1},{U{1} objective}); end function [u, ctrl_info] = eval(obj,x) %% evaluate control action by solving MPC problem, e.g. diff --git a/templates/MPC_TS_SC.m b/templates/MPC_TS_SC.m index 0e64767..fb1c720 100644 --- a/templates/MPC_TS_SC.m +++ b/templates/MPC_TS_SC.m @@ -14,22 +14,58 @@ classdef MPC_TS_SC methods function obj = MPC_TS_SC(Q,R,N,H,h,S,v,params) % YOUR CODE HERE + % initialize parameters + nu = params.model.nu; + nx = params.model.nx; + A=params.model.A; + B=params.model.B; + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; + [~,P,~] = dlqr(A,B,Q,R); + + U = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + X = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + sv = sdpvar(repmat(length(S(1,:)),1,N+1),ones(1,N+1),'full'); + + X0 = sdpvar(nx,1,'full'); + objective = 0; + constraints = X{1} == X0; + % items for 1 to N + for k=1:N + objective = objective + X{k}' * Q * X{k} + U{k}' * R * U{k} + sv{k}' * S * sv{k} + v * max(sv{k}); + constraints = [constraints, ... + X{k+1} == A * X{k} + B * U{k}, ... + H_x * X{k} <= h_x+sv{k}, ... + H_u * U{k} <= h_u, ... + sv{k} >= 0 ... + ]; + end + % items for N+1 + objective = objective + X{N+1}'*P*X{N+1} + sv{N+1}'*S*sv{N+1} + v*max(sv{N+1}); + constraints = [constraints, ... + sv{N+1} >= 0, ... + H_x * X{N+1} <= h_x + sv{N+1} ... + ]; + % maximum positively invariant set constraint + constraints = [constraints, H * X{N+1} <= h]; opts = sdpsettings('verbose',1,'solver','quadprog','quadprog.TolFun',1e-8); obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{U{1} objective}); end function [u, ctrl_info] = eval(obj,x) - %% evaluate control action by solving MPC problem, e.g. + % evaluate control action by solving MPC problem tic; - [optimizer_out,errorcode] = obj.yalmip_optimizer(x); + [optimizer_out,errorcode,~] = obj.yalmip_optimizer{x}; solvetime = toc; + [u, objective] = optimizer_out{:}; feasible = true; if (errorcode ~= 0) feasible = false; end - ctrl_info = struct('ctrl_feas',feasible,'objective',objective,'solvetime',solvetime); end end diff --git a/templates/MPC_TS_SC_params.mat b/templates/MPC_TS_SC_params.mat Binary files differnew file mode 100644 index 0000000..b8cc020 --- /dev/null +++ b/templates/MPC_TS_SC_params.mat diff --git a/templates/MPC_TS_SC_script.m b/templates/MPC_TS_SC_script.m new file mode 100644 index 0000000..9499cf1 --- /dev/null +++ b/templates/MPC_TS_SC_script.m @@ -0,0 +1,14 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Copyright (c) 2023, Amon Lahr, Simon Muntwiler, Antoine Leeman & Fabian Flürenbrock Institute for Dynamic Systems and Control, ETH Zurich. +% +% All rights reserved. +% +% Please see the LICENSE file that has been included as part of this package. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +S=100000000*eye(6); +v=100000000; +matfile=struct("S",S,"v",v); +save("MPC_TS_SC_params.mat","-struct","matfile") + + diff --git a/templates/MPC_TUBE.m b/templates/MPC_TUBE.m index bd62044..9a630c1 100644 --- a/templates/MPC_TUBE.m +++ b/templates/MPC_TUBE.m @@ -15,8 +15,48 @@ classdef MPC_TUBE methods function obj = MPC_TUBE(Q,R,N,H_N,h_N,H_tube,h_tube,K_tube,params) obj.K_tube = K_tube; - + % YOUR CODE HERE + nx = params.model.nx; + nu = params.model.nu; + + A = params.model.A; + B = params.model.B; + + [~,P,~] = dlqr(A,B,Q,R); + + V = sdpvar(repmat(nu,1,N),ones(1,N),'full'); + Z = sdpvar(repmat(nx,1,N+1),ones(1,N+1),'full'); + + H_x = params.constraints.StateMatrix; + h_x = params.constraints.StateRHS; + H_u = params.constraints.InputMatrix; + h_u = params.constraints.InputRHS; + + P_x_tightened = Polyhedron('A',H_x,'b',h_x).minus(Polyhedron('A',H_tube,'b',h_tube)); + H_z = P_x_tightened.A; + h_z = P_x_tightened.b; + + P_u_tightened = Polyhedron('A',H_u,'b',h_u).minus(K_tube*Polyhedron('A',H_tube,'b',h_tube)); + H_v = P_u_tightened.A; + h_v = P_u_tightened.b; + + X0 = sdpvar(nx,1,'full'); + constraints = [H_tube*(X0-Z{1}) <= h_tube]; + objective = 0; + for k = 1:N + constraints = [ ... + constraints, ... + Z{k+1} == A*Z{k} + B*V{k} , ... +% H_z * Z{k} <= h_z, ... +% H_v * V{k} <= h_v ... + H_x * Z{k} <= h_x, ... + H_u * V{k} <= h_u ... + ]; + objective = objective + Z{k}'*Q*Z{k} + V{k}'*R*V{k}; + end + constraints = [constraints, H_N * Z{end} <= h_N]; + objective = objective + Z{end}'*P*Z{end}; opts = sdpsettings('verbose',1,'solver','quadprog'); obj.yalmip_optimizer = optimizer(constraints,objective,opts,X0,{V{1} Z{1} objective}); @@ -28,7 +68,10 @@ classdef MPC_TUBE [optimizer_out,errorcode] = obj.yalmip_optimizer(x); solvetime = toc; % YOUR CODE HERE - + [v0, z0, objective] = optimizer_out{:}; + u = obj.K_tube*(x-z0)+v0; + + feasible = true; if (errorcode ~= 0) feasible = false; diff --git a/templates/MPC_TUBE_params.mat b/templates/MPC_TUBE_params.mat Binary files differnew file mode 100644 index 0000000..9db7ef4 --- /dev/null +++ b/templates/MPC_TUBE_params.mat diff --git a/templates/MPC_TUBE_script.m b/templates/MPC_TUBE_script.m new file mode 100644 index 0000000..a021cd0 --- /dev/null +++ b/templates/MPC_TUBE_script.m @@ -0,0 +1,15 @@ +p = [0.05, 0.1]; +params = generate_params(); +params = generate_params_z(params); +K_tube = compute_tube_controller(p,params); +[H_tube, h_tube, n_iter] = compute_minRPI(K_tube, params); +params = compute_tightening(K_tube, H_tube, h_tube, params); + +Q = diag([300,0.1]);R = 1;N = 50; +[H_N, h_N] = lqr_maxPI(Q, R, params); + +% MPC_TUBE_obj = MPC_TUBE(Q,R,N,H_N,h_N,H_tube,h_tube,K_tube,params); +matfile = struct("p", p, "K_tube", K_tube, "H_tube", H_tube, "h_tube", h_tube,... + "H_N", H_N, "h_N", h_N, "params_z_tube", params); +save("MPC_TUBE_params.mat", "-struct", "matfile"); + diff --git a/templates/chebycenter.m b/templates/chebycenter.m new file mode 100755 index 0000000..cbdce1c --- /dev/null +++ b/templates/chebycenter.m @@ -0,0 +1,20 @@ +function [c,r] = chebycenter(A,b) +%CHEBYCENTER Compute Chebyshev center of polytope Ax <= b. +% The Chebyshev center of a polytope is the center of the largest +% hypersphere enclosed by the polytope. +% Requires optimization toolbox. + +[n,p] = size(A); +an = sqrt(sum(A.^2,2)); +A1 = zeros(n,p+1); +A1(:,1:p) = A; +A1(:,p+1) = an; +f = zeros(p+1,1); +f(p+1) = -1; + +options = optimset; +options = optimset(options,'Display', 'off'); +c = linprog(f,A1,b,[],[],[],[],[],options); +r = c(p+1); +c = c(1:p); +end diff --git a/templates/compute_minRPI.m b/templates/compute_minRPI.m index 0b4ffdb..19df517 100644 --- a/templates/compute_minRPI.m +++ b/templates/compute_minRPI.m @@ -8,4 +8,32 @@ function [H_tube,h_tube,n_iter] = compute_minRPI(K_tube,params) % YOUR CODE HERE + A = params.model.A+params.model.B*K_tube; + % A = params.model.A; +% display(A) + nx = params.model.nx; + omega = Polyhedron('A',[eye(nx);-eye(nx)],'b',zeros(1,2*nx)'); + % display(omega.A) + % display(omega.b) + n_iter = 0; + Hw = params.constraints.DisturbanceMatrix; + hw = params.constraints.DisturbanceRHS; + W = Polyhedron('A',Hw,'b',hw); + while true + omega_last = copy(omega); + % display(n_iter) + % A_last = omega.A; + % b_last = omega.b; + display(n_iter); + display(omega.b) + omega = omega.plus(A^(n_iter)*W); + + if eq(omega.minHRep(),omega_last.minHRep()) + % if eq(omega,omega_last) + break + end + n_iter = n_iter+1; + end + H_tube = omega.A; + h_tube = omega.b; end
\ No newline at end of file diff --git a/templates/compute_tightening.m b/templates/compute_tightening.m index 8919d12..7095f9c 100644 --- a/templates/compute_tightening.m +++ b/templates/compute_tightening.m @@ -8,4 +8,22 @@ function params = compute_tightening(K_tube,H_tube,h_tube,params) % YOUR CODE HERE + Hx = params.constraints.StateMatrix; + hx = params.constraints.StateRHS; + + Hu = params.constraints.InputMatrix; + hu = params.constraints.InputRHS; + + Pxz = Polyhedron('A',Hx,'b',hx); + Puz = Polyhedron('A',Hu,'b',hu); + % Ptube = Polyhedron('A',H_tube,'b',h_tube); + + Px_tube = Pxz.minus(Polyhedron('A',H_tube,'b',h_tube)); + params.constraints.StateMatrix = Px_tube.A; + params.constraints.StateRHS = Px_tube.b; + + Pu_tube = Puz.minus(K_tube*Polyhedron('A',H_tube,'b',h_tube)) +% Pu_tube = Puz.minus(Polyhedron('A',H_tube*K_tube,'b',h_tube)); + params.constraints.InputMatrix = Pu_tube.A; + params.constraints.InputRHS = Pu_tube.b; end
\ No newline at end of file diff --git a/templates/compute_tube_controller.m b/templates/compute_tube_controller.m index adca95d..2c567f0 100644 --- a/templates/compute_tube_controller.m +++ b/templates/compute_tube_controller.m @@ -8,4 +8,9 @@ function K_tube = compute_tube_controller(p,params) % YOUR CODE HERE + Az = params.model.A; + Bz =params.model.B; + % Bz = [params.model.B,eye(params.model.nx)]; + K_tube = -place(Az,Bz,p); + % K_tube = K(1:params.model.nu,:); end
\ No newline at end of file diff --git a/templates/cprnd.m b/templates/cprnd.m new file mode 100755 index 0000000..4183ac3 --- /dev/null +++ b/templates/cprnd.m @@ -0,0 +1,296 @@ +function [X S] = cprnd(N,A,b,options) +%CPRND Draw from the uniform distribution over a convex polytope. +% X = cprnd(N,A,b) Returns an N-by-P matrix of random vectors drawn +% from the uniform distribution over the interior of the polytope +% defined by Ax <= b. A is a M-by-P matrix of constraint equation +% coefficients. b is a M-by-1 vector of constraint equation +% constants. +% +% cprnd(N,A,b,options) allows various options to be specified. + +% 'method' Specifies the algorithm. One of the strings 'gibbs', +% 'hitandrun' (the default), and 'achr'. The default +% algorithm 'hitandrun' is a vanilla hit-and-run sampler +% [1]. 'gibbs' specifies a Gibbs sampler, 'achr' is the +% Adaptive Centering Hit-and-Run algorithm of [2]. +% +% 'x0' Vector x0 is a starting point which should be interior +% to the polytope. If x0 is not supplied CPRND uses the +% Chebyshev center as the initial point. +% +% 'isotropic' Perform an adaptive istropic transformation of the +% polytope. The values 0, 1 and 2 respectively turn +% off the transformation, construct it during a runup +% period only, or continuously update the +% tranformation throughout sample production. The +% transformation makes sense only for the Gibbs and +% Hit-and-run samplers (ACHR is invariant under +% linear transformations). +% +% 'discard' Number of initial samples (post-runup) to discard. +% +% 'runup' When the method is gibbs or hitandrun and the +% isotropic transformation is used, this is the +% number of initial iterations of the algorithm in +% the untransformed space. That is a sample of size +% runup is generated and its covariance used as the +% basis of a transformation. +% When the method is achr runup is the number of +% conventional hitandrun iterations. See [2]. +% +% 'ortho' Zero/one flag. If turned on direction vectors for +% the hitandrun algorithm are generated in random +% orthonormal blocks rather than one by +% one. Experimental and of dubious utility. +% +% 'quasi' Allows the user to specify a quasirandom number generator +% (such as 'halton' or 'sobol'). Experimental and of +% dubious utility. +% +% + +% By default CPRND employs the hit-and-run sampler which may +% exhibit marked serial correlation and very long convergence times. +% +% References +% [1] Kroese, D.P. and Taimre, T. and Botev, Z.I., "Handbook of Monte +% Carlo Methods" (2011), pp. 240-244. +% [2] Kaufman, David E. and Smith, Robert L., "Direction Choice for +% Accelerated Convergence in Hit-and-Run Sampling", Op. Res. 46, +% pp. 84-95. +% +% Copyright (c) 2011-2012 Tim J. Benham, School of Mathematics and Physics, +% University of Queensland. + + function y = stdize(z) + y = z/norm(z); + end + + p = size(A,2); % dimension + m = size(A,1); % num constraint ineqs + x0 = []; + runup = []; % runup necessary to method + discard = []; % num initial pts discarded + quasi = 0; + method = 'achr'; + orthogonal = 0; + isotropic = []; + + % gendir generates a random unit (direction) vector. + gendir = @() stdize(randn(p,1)); + + % Alternative function ogendir forces directions to come in + % orthogonal bunches. + Ucache = {}; + function u = ogendir() + if length(Ucache) == 0 + u = stdize(randn(p,1)); + m = null(u'); % orthonormal basis for nullspace + Ucache = mat2cell(m',ones(1,p-1)); + else + u = Ucache{end}'; + Ucache(end) = []; + end + end + + % Check input arguments + + if m < p+1 + % obv a prob here + error('cprnd:obvprob',['At least ',num2str(p+1),' inequalities ' ... + 'required']); + end + + if nargin == 4 + if isstruct(options) + + if isfield(options,'method') + method = lower(options.method); + switch method + case 'gibbs' + case 'hitandrun' + case 'achr' + otherwise + error('cprnd:badopt',... + ['The method option takes only the ' ... + 'values "gibbs", "hitandrun", and "ACHR".']); + end + end + + if isfield(options,'isotropic') + % Controls application of isotropic transformation, + % which seems to help a lot. + isotropic = options.isotropic; + end + + if isfield(options,'discard') + % num. of samples to discard + discard = options.discard; + end + + if isfield(options,'quasi') + % Use quasi random numbers, which doesn't seem to + % help much. + quasi = options.quasi; + if quasi && ~ischar(quasi), quasi='halton'; end + if ~strcmp(quasi,'none') + qstr = qrandstream(quasi,p,'Skip',1); + gendir = @() stdize(norminv(qrand(qstr,1),0,1)'); + end + end + + if isfield(options,'x0') + % initial interior point + x0 = options.x0; + end + + if isfield(options,'runup') + % number of points to generate before first output point + runup = options.runup; + end + + if isfield(options,'ortho') + % Generate direction vectors in orthogonal + % groups. Seems to help a little. + orthogonal = options.ortho; + end + + else + x0 = options; % legacy support + end + end + + % Default and apply options + + if isempty(isotropic) + if ~strcmp(method,'achr') + isotropic = 2; + else + isotropic = 0; + end + end + + if orthogonal + gendir = @() ogendir(); + end + + % Choose a starting point x0 if user did not provide one. + if isempty(x0) + x0 = chebycenter(A,b); % prob. if p==1? + end + + % Default the runup to something arbitrary. + if isempty(runup) + if strcmp(method,'achr') + runup = 10*(p+1); + elseif isotropic > 0 + runup = 10*p*(p+1); + else + runup = 0; + end + end + + % Default the discard to something arbitrary + if isempty(discard) + if strcmp(method,'achr') + discard = 25*(p+1); + else + discard = runup; + end + end + + X = zeros(N+runup+discard,p); + + n = 0; % num generated so far + x = x0; + + % Initialize variables for keeping track of sample mean, covariance + % and isotropic transform. + M = zeros(p,1); % Incremental mean. + S2 = zeros(p,p); % Incremental sum of + % outer prodcts. + S = eye(p); T = eye(p); W = A; + + while n < N+runup+discard + y = x; + + % compute approximate stochastic transformation + if isotropic>0 + if n == runup || (isotropic > 1 && n > runup) + T = chol(S,'lower'); + W = A*T; + end + y = T\y; + end + + switch method + + case 'gibbs' + % choose p new components + for i = 1:p + % Find points where the line with the (p-1) components x_i + % fixed intersects the bounding polytope. + e = circshift(eye(p,1),i-1); + z = W*e; + c = (b - W*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % choose a point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*e; + end + + case 'hitandrun' + % choose a direction + u = gendir(); + % determine intersections of x + ut with the polytope + z = W*u; + c = (b - W*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % choose a point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*u; + + case 'achr' + % test whether in runup or not + if n < runup + % same as hitandrun + u = gendir(); + else + % choose a previous point at random + v = X(randi(n),:)'; + % line sampling direction is from v to sample mean + u = (v-M)/norm(v-M); + end + % proceed as in hit and run + z = A*u; + c = (b - A*y)./z; + tmin = max(c(z<0)); tmax = min(c(z>0)); + % Choose a random point on that line segment + y = y + (tmin+(tmax-tmin)*rand)*u; + end + + if isotropic>0 + x = T*y; + else + x = y; + end + + X(n+1,:)=x'; + n = n + 1; + + % Incremental mean and covariance updates + delta0 = x - M; % delta new point wrt old mean + M = M + delta0/n; % sample mean + delta1 = x - M; % delta new point wrt new mean + if n > 1 + S2 = S2 + (n-1)/(n*n)*delta0*delta0'... + + delta1*delta1'; + S0 = S; + S = S2/(n-1); % sample covariance + else + S = eye(p); + end + + end + + X = X((discard+runup+1):(N+discard+runup),:); + +end diff --git a/templates/generate_constraints.m b/templates/generate_constraints.m index 892b706..e2e4357 100644 --- a/templates/generate_constraints.m +++ b/templates/generate_constraints.m @@ -7,5 +7,10 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [H_u, h_u, H_x, h_x] = generate_constraints(params) - % YOUR CODE HERE + H_u = [eye(params.model.nu); -eye(params.model.nu)]; + h_u = params.constraints.MaxAbsThrust * ones(params.model.nu*2,1); + + H_x = [eye(3), zeros(3); -eye(3), zeros(3)]; % * inv(params.model.ScalingMatrix); + h_x = params.constraints.MaxAbsPositionXZ * [1, 0, 1, 1, 0, 1].' + ... + params.constraints.MaxAbsPositionY * [0, 1, 0, 0, 1, 0].'; end
\ No newline at end of file diff --git a/templates/generate_disturbances.m b/templates/generate_disturbances.m index 570a4c9..f08cdb5 100644 --- a/templates/generate_disturbances.m +++ b/templates/generate_disturbances.m @@ -8,4 +8,10 @@ function Wt = generate_disturbances(params) % YOUR CODE HERE + % params_z = generate_params_z(params); + Hw = params.constraints.DisturbanceMatrix; + hw = params.constraints.DisturbanceRHS; + % Pw = Polyhedron('A', Hw, 'b', hw); + N = params.model.HorizonLength; + Wt = cprnd(N,Hw,hw)'; end
\ No newline at end of file diff --git a/templates/generate_params.m b/templates/generate_params.m index ef51366..4b61e31 100644 --- a/templates/generate_params.m +++ b/templates/generate_params.m @@ -40,6 +40,19 @@ params.exercise = struct( ... 'QdiagOptA', [94.0; 0.1579; 300; 0.01; 0.10; 0.10] ... ); -% YOUR CODE HERE +% Add system model +[Ac, Bc] = generate_system_cont(params); +[At, Bt] = generate_system(Ac, Bc, params); +[A, B] = generate_system_scaled(At, Bt, params); + +params.model.A = A; +params.model.B = B; + +% Add constraints +[H_u, h_u, H_x, h_x] = generate_constraints(params); +params.constraints.InputMatrix = H_u; +params.constraints.InputRHS = h_u; +params.constraints.StateMatrix = H_x; +params.constraints.StateRHS = h_x; end diff --git a/templates/generate_system.m b/templates/generate_system.m index 9deb347..b44bef2 100644 --- a/templates/generate_system.m +++ b/templates/generate_system.m @@ -7,5 +7,9 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [A, B] = generate_system(Ac, Bc, params) - % YOUR CODE HERE -end
\ No newline at end of file + sys = ss(Ac, Bc, eye(params.model.nx), zeros(params.model.nx, params.model.nu)); + sysd = c2d(sys, params.model.TimeStep); + + A = sysd.A; + B = sysd.B; +end diff --git a/templates/generate_system_cont.m b/templates/generate_system_cont.m index 2d3ee79..048ee7b 100644 --- a/templates/generate_system_cont.m +++ b/templates/generate_system_cont.m @@ -7,5 +7,16 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [Ac, Bc] = generate_system_cont(params) - % YOUR CODE HERE -end
\ No newline at end of file + % YOUR CODE HERE + omega_n_sq = params.model.GravitationalParameter / params.model.TargetRadius^3; + omega_n = sqrt(omega_n_sq); + + Ac = [ + zeros(3), eye(3); + 3*omega_n_sq, 0, 0, 0, 2*omega_n, 0; + 0, 0, 0, -2*omega_n, 0, 0; + 0, 0, -omega_n_sq, 0, 0, 0; + ]; + + Bc = [zeros(3); eye(3);] / params.model.Mass; +end diff --git a/templates/generate_system_scaled.m b/templates/generate_system_scaled.m index eac8db8..d65c7b3 100644 --- a/templates/generate_system_scaled.m +++ b/templates/generate_system_scaled.m @@ -6,6 +6,11 @@ % Please see the LICENSE file that has been included as part of this package. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -function [A,B] = generate_system_scaled(At,Bt,params) +function [A, B] = generate_system_scaled(At, Bt, params) % YOUR CODE HERE -end
\ No newline at end of file + V = params.model.ScalingMatrix; + Vinv = inv(V); + + A = V*At*Vinv; + B = V*Bt; +end diff --git a/templates/lqr_maxPI.m b/templates/lqr_maxPI.m index efa335a..99b5b22 100644 --- a/templates/lqr_maxPI.m +++ b/templates/lqr_maxPI.m @@ -6,7 +6,40 @@ % Please see the LICENSE file that has been included as part of this package. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -function [H, h] = lqr_maxPI(Q,R,params) - % YOUR CODE HERE + +function [H, h] = lqr_maxPI(Q, R, params) + % Define the linear system + A = params.model.A; + B = params.model.B; + nx=params.model.nx; + nu=params.model.nu; + + s_max= params.constraints.MaxAbsPositionXZ; + y_max= params.constraints.MaxAbsPositionY; + u_max = params.constraints.MaxAbsThrust; + + K = -dlqr(A, B, Q, R); + systemLQR = LTISystem('A', A+B*K); +% absxmax = ones(nx,1)*s_max; +% absumax = ones(nu,1)*u_max; +% Xp = Polyhedron('A',[eye(nx); -eye(nx); K; -K], 'b', [absxmax;absxmax; absumax;absumax]); + Hx=params.constraints.StateMatrix; + hx=params.constraints.StateRHS; + Hu=params.constraints.InputMatrix; + hu=params.constraints.InputRHS; + Xp = Polyhedron('A',[Hx;Hu*K], 'b', [hx;hu]); + + figure(1); + systemLQR.x.with('setConstraint'); + systemLQR.x.setConstraint = Xp; + InvSetLQR = systemLQR.invariantSet(); +% InvSetLQR.plot(), alpha(0.25), title('Invariant Set for Triple Integrator under LQR Control'), xlabel('x_1'), ylabel('x_2'), zlabel('x_3'); + + H=InvSetLQR.A; + h=InvSetLQR.b; + + end + + diff --git a/templates/lqr_tuning.m b/templates/lqr_tuning.m index 4a26158..9c9aab9 100644 --- a/templates/lqr_tuning.m +++ b/templates/lqr_tuning.m @@ -8,4 +8,48 @@ function [tuning_struct, i_opt] = lqr_tuning(x0,Q,params) % YOUR CODE HERE -end
\ No newline at end of file + i_opt = nan; + best_J_u = inf; + + % Prepare an array of empty structs + tuning_struct = repmat(struct( ... + 'InitialCondition', {}, ... + 'Qdiag', {}, ... + 'MaxAbsPositionXZ', {}, ... + 'MaxAbsPositionY', {}, ... + 'MaxAbsThrust', {}, ... + 'InputCost', {}, ... + 'MaxFinalPosDiff', {}, ... + 'MaxFinalVelDiff', {}, ... + 'TrajFeasible', {} ... + ), size(Q,2), 1); + + for i=1:size(Q,2) + tuning_struct(i).InitialCondition = x0; + tuning_struct(i).Qdiag = Q(:,i); + + ctrl = LQR(diag(Q(:,i)), eye(params.model.nu), params); + [Xt, Ut, ~] = simulate(x0, ctrl, params); + + [s_max, y_max, u_max, J_u, df_max, vf_max, traj_feas] = ... + traj_constraints(Xt, Ut, params); + + tuning_struct(i).MaxAbsPositionXZ = s_max; + tuning_struct(i).MaxAbsPositionY = y_max; + tuning_struct(i).MaxAbsThrust = u_max; + tuning_struct(i).InputCost = J_u; + tuning_struct(i).MaxFinalPosDiff = df_max; + tuning_struct(i).MaxFinalVelDiff = vf_max; + tuning_struct(i).TrajFeasible = traj_feas; + + if traj_feas + if J_u < best_J_u + i_opt = i; + best_J_u = J_u; + end + end + end + + % because the test suite wants a column vector + tuning_struct = tuning_struct'; +end diff --git a/templates/lqr_tuning_script.m b/templates/lqr_tuning_script.m new file mode 100644 index 0000000..4a02fc6 --- /dev/null +++ b/templates/lqr_tuning_script.m @@ -0,0 +1,58 @@ +function [tuning_struct] = lqr_tuning_script(params) + % From the hint: look in the vicinity of vector from the next section + % also from the hint: qx, qy, qvx, qvy are decoupled from qz, qvz + q_start = [94, .1579, 300, .01, .1, .1]; + + % parameters for sampling + v = 0.4; % search around q +- v * q + nsamples = 3; + + q = q_start; + best_J_u = inf; + while best_J_u > 7.6 + % Create sampling grid + range = linspace(1-v, 1+v, nsamples)'; + + % Sample in qx qy qvx qvy + G = kron(q([1,2,4,5]), range); + [Sx, Sy, Svx, Svy] = ndgrid(G(:,1), G(:,2), G(:,3), G(:,4)); + Q = [Sx(:), Sy(:), q(3) * ones(size(Sx(:))), ... + Svx(:), Svy(:), q(6) * ones(size(Sx(:)))]'; + + % Find best q + [ts, i_opt] = lqr_tuning(params.model.InitialConditionA, Q, params); + + % Save new best solution + if ~ isnan(i_opt) + tuning_struct = ts(i_opt); + best_J_u = ts(i_opt).InputCost; + q = ts(i_opt).Qdiag'; + end + + % Sample in qz qvz + G = kron(q([3,6]), range); + [Sz, Svz] = ndgrid(G(:,1), G(:,2)); + qs = kron(q, ones(size(Sz(:)))); + Q = [qs(:,1:2), Sz(:), qs(:,3:4), Svz(:)]'; + + % Find best item + [ts, i_opt] = lqr_tuning(params.model.InitialConditionA, Q, params); + + % Save new best solution + if ~ isnan(i_opt) + tuning_struct = ts(i_opt); + best_J_u = ts(i_opt).InputCost; + q = ts(i_opt).Qdiag'; + end + + % Search in a narrower region, increase resolution + v = v / 2; + + % Log + fprintf("Lowest J_u so far: %d, searching with v=%f\n", best_J_u,v); + end + + % Save for test + matfile = struct("tuning_struct", tuning_struct, "q", tuning_struct.Qdiag); + save("lqr_tuning_script.mat", "-struct", "matfile"); +end diff --git a/templates/lqr_tuning_script.mat b/templates/lqr_tuning_script.mat Binary files differnew file mode 100644 index 0000000..af9681c --- /dev/null +++ b/templates/lqr_tuning_script.mat diff --git a/templates/simulate.m b/templates/simulate.m index 3138cd1..6be40c3 100644 --- a/templates/simulate.m +++ b/templates/simulate.m @@ -7,8 +7,17 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [Xt,Ut,ctrl_info] = simulate(x0, ctrl, params) + % YOUR CODE HERE + % Hint: you can access the control command with ctrl.eval(x(:,i)) -% YOUR CODE HERE -% Hint: you can access the control command with ctrl.eval(x(:,i)) + Xt = zeros(params.model.nx, params.model.HorizonLength+1); + Ut = zeros(params.model.nu, params.model.HorizonLength); + ctrl_info = repmat(struct('ctrl_feas',true), 1, params.model.HorizonLength); -end
\ No newline at end of file + Xt(:,1) = x0; + for k=1:params.model.HorizonLength + [u, ~] = ctrl.eval(Xt(:,k)); + Ut(:,k) = u; + Xt(:,k+1) = params.model.A * Xt(:,k) + params.model.B * Ut(:,k); + end +end diff --git a/templates/simulate_uncertain.m b/templates/simulate_uncertain.m index dc9df26..f74f7af 100644 --- a/templates/simulate_uncertain.m +++ b/templates/simulate_uncertain.m @@ -8,4 +8,17 @@ function [Xt,Ut,ctrl_info] = simulate_uncertain(x0, ctrl, Wt, params) % YOUR CODE HERE + Xt = [x0]; + Ut = []; + x = x0 + ctrl_info = []; + % obj = LQR(); + for i = 1:params.model.HorizonLength + [u, ctrl_info_] = ctrl.eval(x); + Ut = [Ut u]; + ctrl_info = [ctrl_info ctrl_info_]; + x = params.model.A*x + params.model.B*u + Wt(:,i); + Xt = [Xt x]; + end + % plot_trajectory(Xt, Ut, ctrl_info, params); end
\ No newline at end of file diff --git a/templates/traj_constraints.m b/templates/traj_constraints.m index 4b0a081..69d19d3 100644 --- a/templates/traj_constraints.m +++ b/templates/traj_constraints.m @@ -8,5 +8,33 @@ function [s_max, y_max, u_max, J_u, df_max, vf_max, traj_feas] = traj_constraints(x,u,params) % YOUR CODE HERE + + s_max = max(max(abs(x([1,3],:)))); + y_max = max(abs(x(2,:))); + u_max = max(max(abs(u))); + + J_u = 0; + for k=1:size(u,2) + J_u = J_u + u(:,k)' * u(:,k); + end + + df_max = sqrt(sum(x(1:3,end).^2)); + vf_max = sqrt(sum(x(4:6,end).^2)); + + constr = [ + s_max <= params.constraints.MaxAbsPositionXZ, ... + y_max <= params.constraints.MaxAbsPositionY, ... + u_max <= params.constraints.MaxAbsThrust, ... + df_max <= params.constraints.MaxFinalPosDiff, ... + vf_max <= params.constraints.MaxFinalVelDiff + ]; + + % disp([s_max, y_max, df_max, vf_max]) + % disp([params.constraints.MaxAbsPositionXZ, ... + % params.constraints.MaxAbsPositionY, ... + % params.constraints.MaxFinalPosDiff, ... + % params.constraints.MaxFinalVelDiff]) + % disp(constr') + traj_feas = all(constr); end diff --git a/templates/traj_cost.m b/templates/traj_cost.m index 7e0b443..57566c9 100644 --- a/templates/traj_cost.m +++ b/templates/traj_cost.m @@ -8,4 +8,10 @@ function J_Nt = traj_cost(Xt,Ut,Q,R) % YOUR CODE HERE + J_Nt=0; + for i=1:length(Xt(1,:))-1 + a= Xt(:,i)'*Q*Xt(:,i); + b= Ut(:,i)'*R*Ut(:,i); + J_Nt=J_Nt+a+b; + end end
\ No newline at end of file |