From 1f12e47e6d1fe8b365806aa0b42de237970d53bf Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Wed, 24 May 2023 16:50:06 +0200 Subject: Take deliverables for Robust MPC from yanzhen According to table 12 - generate_disturbances - simulate_uncertain - compute_tube_contorller - compute_minRPI - compute_tightening - MPC_TUBE - MPC_TUBE/eval (contained in MPC_TUBE.m) - MPC_TUBE_script (and its output MPC_TUBE_params.mat) --- templates/MPC_TUBE.m | 47 +++++- templates/MPC_TUBE_params.mat | Bin 0 -> 1537 bytes templates/MPC_TUBE_script.m | 15 ++ templates/chebycenter.m | 20 +++ templates/compute_minRPI.m | 28 ++++ templates/compute_tightening.m | 18 +++ templates/compute_tube_controller.m | 5 + templates/cprnd.m | 296 ++++++++++++++++++++++++++++++++++++ templates/generate_disturbances.m | 6 + templates/simulate_uncertain.m | 13 ++ 10 files changed, 446 insertions(+), 2 deletions(-) create mode 100644 templates/MPC_TUBE_params.mat create mode 100644 templates/MPC_TUBE_script.m create mode 100755 templates/chebycenter.m create mode 100755 templates/cprnd.m (limited to 'templates') 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 new file mode 100644 index 0000000..9db7ef4 Binary files /dev/null and b/templates/MPC_TUBE_params.mat differ 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_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/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 -- cgit v1.2.1