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authorYuan Xu <yuanxu@student.ethz.ch>2023-05-24 17:35:46 +0200
committerYuan Xu <yuanxu@student.ethz.ch>2023-05-24 17:35:46 +0200
commita23ba49056a36aff221d0c23e228b981222c3576 (patch)
tree742c18cbe13c1603909b55ee82188ce6360e8fa0 /Submission files
parentADD: declaration of originality (diff)
downloadmpc_pe-submission.tar.gz
mpc_pe-submission.zip
add submission zipsubmission
Diffstat (limited to '')
-rw-r--r--Submission files/LQR.m31
-rw-r--r--Submission files/MPC.m71
-rw-r--r--Submission files/MPC_TE.m62
-rw-r--r--Submission files/MPC_TE_forces.m38
-rw-r--r--Submission files/MPC_TS.m62
-rw-r--r--Submission files/MPC_TS_SC.m72
-rw-r--r--Submission files/MPC_TS_SC_script.m14
-rw-r--r--Submission files/MPC_TUBE.m83
-rw-r--r--Submission files/MPC_TUBE_script.m15
-rw-r--r--Submission files/chebycenter.m20
-rw-r--r--Submission files/compute_minRPI.m39
-rw-r--r--Submission files/compute_tightening.m29
-rw-r--r--Submission files/compute_tube_controller.m16
-rw-r--r--Submission files/cprnd.m296
-rw-r--r--Submission files/declaration-originality.pdf3757
-rw-r--r--Submission files/generate_constraints.m16
-rw-r--r--Submission files/generate_disturbances.m17
-rw-r--r--Submission files/generate_params.m58
-rw-r--r--Submission files/generate_params_z.m55
-rw-r--r--Submission files/generate_system.m15
-rw-r--r--Submission files/generate_system_cont.m22
-rw-r--r--Submission files/generate_system_scaled.m16
-rw-r--r--Submission files/lqr_maxPI.m45
-rw-r--r--Submission files/lqr_tuning.m55
-rw-r--r--Submission files/lqr_tuning_script.m58
-rw-r--r--Submission files/plot_trajectory.m126
-rw-r--r--Submission files/plot_trajectory_z.m78
-rw-r--r--Submission files/simulate.m23
-rw-r--r--Submission files/simulate_uncertain.m24
-rw-r--r--Submission files/test_struct.matbin0 -> 17506 bytes
-rw-r--r--Submission files/traj_constraints.m40
-rw-r--r--Submission files/traj_cost.m17
32 files changed, 5270 insertions, 0 deletions
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 0000000..42f9e64
--- /dev/null
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@@ -0,0 +1,3757 @@
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diff --git a/Submission files/generate_constraints.m b/Submission files/generate_constraints.m
new file mode 100644
index 0000000..e2e4357
--- /dev/null
+++ b/Submission files/generate_constraints.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 [H_u, h_u, H_x, h_x] = generate_constraints(params)
+ 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/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
new file mode 100644
index 0000000..14d32f6
--- /dev/null
+++ b/Submission files/test_struct.mat
Binary files differ
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 \ No newline at end of file