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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
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