1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
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
|
