yalmip('clear')
clear all

% Prediction horizon
N = 5;

opt_sincos

probStruct.N=N-1;

ctrl=mpt_control(sysStruct,probStruct)

nx = 2;
nu = 1;

% 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));

% Binary for PWA selection
d = binvar(2,1);

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

% Initialize value function at stage N
J{N} = 0;

for k = N-1:-1:1
    % Feasible region
     t = sdpvar(2,1);
     bounds(x{k},sysStruct.xmin,sysStruct.xmax);
     bounds(u{k},sysStruct.umin,sysStruct.umax);
     bounds(x{k+1},sysStruct.xmin,sysStruct.ymax);
     bounds(t,0,60);
    
    F =     set(sysStruct.umin < u{k}     < sysStruct.umax);
    F = F + set(sysStruct.xmin < x{k}     < sysStruct.xmax);    
    F = F + set(sysStruct.xmin < x{k+1}   < sysStruct.xmax);    
    F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k}   < sysStruct.ymax);    
    F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax);

    F = F + set(-t(1) < x{k} < t(1)) ;
    F = F + set(-t(2) < u{k} < t(2)) ;
    
    % PWA Dynamics
    for i = 1:length(sysStruct.A)
        F = F + set(implies(d(i),x{k+1} == sysStruct.A{i}*x{k}+sysStruct.B{i}*u{k}+sysStruct.f{i}));
        F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} < sysStruct.guardC{i}));
    end
    F = F + set(sum(d) == 1);

    % Compute value function for one step backwards
    [mpsol{k},sol{k},Uz{k},J{k},U{k}] = solvemp(F,sum(t) + J{k+1},[],x{k},u{k});

end

mpsol{1} = rmovlps(mpsol{1})

mpt_isPWAbigger(mpsol{1},ctrl)

%mpt_plotpwA(mpsol{k}.Pn,mpsol{k}.Bi,mpsol{k}.Ci);hold on
%mpt_plotpwA(ctrl.Pn,ctrl.Bi,ctrl.Ci)