source: proiecte/pmake3d/make3d_original/Make3dSingleImageStanford_version0.1/third_party/opt/yalmip/dev/tests-mbg/mpt/mpt_lti_2.m @ 37

function dplti_1 

% Data
A = [2 -1;1 0];nx = 2;
B = [1;0];nu = 1;
C = [0.5 0.5];

% Prediction horizon
N = 5;

% States x(k), ..., x(k+N)
x = sdpvar(repmat(nx,1,N),repmat(1,1,N));

% Inputs u(k), ..., u(k+N) (last one not used)
u = sdpvar(repmat(nu,1,N),repmat(1,1,N));

% MPT implementation
sysStruct.A= A;
sysStruct.B= B;
sysStruct.C= C;
sysStruct.D= [0];

%set constraints on output
sysStruct.ymin    =   -1;
sysStruct.ymax    =    1;

%set constraints on input
sysStruct.umin    =   -1;
sysStruct.umax    =   1;

sysStruct.xmin    =   [-5;-5];
sysStruct.xmax    =   [5;5];

probStruct.norm=1;
probStruct.Q=eye(2);
probStruct.R=1;
probStruct.N=N-1;
probStruct.P_N=zeros(2);
probStruct.subopt_lev=0;
probStruct.y0bounds=1;
probStruct.Tconstraint=0;
ctrl=mpt_control(sysStruct,probStruct)

% States x(k), ..., x(k+N)
x = sdpvar(repmat(nx,1,N),repmat(1,1,N));

% Inputs u(k), ..., u(k+N) (last one not used)
u = sdpvar(repmat(nu,1,N),repmat(1,1,N));

% Value functions
J = cell(1,N);

% Initialize value function at stage N
J{N} = 0;
F = set([]);
obj = 0;
for k = N-1:-1:1
    % Feasible region
    F = F + set(-1 < u{k}     < 1);
    F = F + set(-1 < C*x{k}   < 1);
    F = F + set(-5 < x{k}     < 5);
    F = F + set(-1 < C*x{k+1} < 1);
    F = F + set(-5 < x{k+1}   < 5);

    % LTI Dynamics
    F = F + set(x{k+1} == A*x{k}+B*u{k});

    % Compute value function for one step backwards
    obj = obj + norm([x{k};u{k}],1);
end
mpsol{1}  = solvemp(F,obj,[],x{k},u{k});
 
mbg_asserttolequal(mpt_isPWAbigger(mpsol{1}{1},ctrl),0);