[37] | 1 | yalmip('clear') |
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| 2 | mpt_init('lpsolver','clp') |
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| 3 | |
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| 4 | % Prediction horizon |
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| 5 | N = 4; |
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| 6 | |
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| 7 | pwa3d |
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| 8 | sysStruct.xmin = sysStruct.ymin; |
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| 9 | sysStruct.xmax = sysStruct.ymax; |
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| 10 | probStruct.R = 1; |
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| 11 | probStruct.N=N-1; |
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| 12 | probStruct.norm = 1; |
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| 13 | probStruct.subopt_lev=0; |
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| 14 | probStruct.P_N = zeros(3); |
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| 15 | if 0 |
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| 16 | ctrl=mpt_control(sysStruct,probStruct) |
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| 17 | end |
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| 18 | nx = 3; |
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| 19 | nu = 1; |
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| 20 | |
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| 21 | % States x(k), ..., x(k+N) |
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| 22 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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| 23 | |
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| 24 | % Inputs u(k), ..., u(k+N) (last one not used) |
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| 25 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 26 | |
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| 27 | % Binary for PWA selection |
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| 28 | d = binvar(2,1); |
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| 29 | |
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| 30 | % Value functions |
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| 31 | J = cell(1,N); |
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| 32 | |
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| 33 | tic |
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| 34 | % Initialize value function at stage N |
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| 35 | J{N} = 0; |
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| 36 | sysStruct.xmin = sysStruct.ymin; |
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| 37 | sysStruct.xmax = sysStruct.ymax; |
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| 38 | for k = N-1:-1:1 |
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| 39 | % Feasible region |
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| 40 | t = sdpvar(nx+nu,1); |
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| 41 | % bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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| 42 | % bounds(u{k},sysStruct.umin,sysStruct.umax); |
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| 43 | % bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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| 44 | % bounds(t,0,600); |
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| 45 | |
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| 46 | F = set(sysStruct.umin < u{k} < sysStruct.umax); |
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| 47 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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| 48 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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| 49 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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| 50 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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| 51 | |
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| 52 | F = F + set(-t < [x{k};u{k}] < t) ; |
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| 53 | F = F + set(0 < t < 600); |
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| 54 | % PWA Dynamics |
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| 55 | for i = 1:length(sysStruct.A) |
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| 56 | F = F + set(implies(d(i),x{k+1} == sysStruct.A{i}*x{k}+sysStruct.B{i}*u{k}+sysStruct.f{i})); |
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| 57 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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| 58 | end |
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| 59 | F = F + set(sum(d) == 1); |
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| 60 | |
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| 61 | % Compute value function for one step backwards |
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| 62 | [mpsol{k},sol{k},Uz{k},J{k}] = solvemp(F,sum(t) + J{k+1},[],x{k},u{k}); |
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| 63 | end |
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| 64 | toc |
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| 65 | break |
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| 66 | |
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| 67 | mpsol{1} = mpt_removeOverlaps(mpsol{1}) |
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| 68 | |
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| 69 | [pass,tol] = mpt_isPWAbigger(mpsol{1},ctrl) |
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| 70 | |
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| 71 | |
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| 72 | |
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| 73 | break |
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| 74 | |
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| 75 | % On-line solution |
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| 76 | nx = 3; |
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| 77 | nu = 1; |
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| 78 | J{N} = 0; |
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| 79 | sysStruct.xmin = sysStruct.ymin; |
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| 80 | sysStruct.xmax = sysStruct.ymax; |
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| 81 | F = set([]); |
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| 82 | obj = 0; |
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| 83 | dd = []; |
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| 84 | for k = N-1:-1:1 |
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| 85 | % Feasible region |
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| 86 | % t = sdpvar(nx+nu,1); |
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| 87 | d = binvar(2,1);dd = [dd;d]; |
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| 88 | % obj = obj + sum(t); |
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| 89 | bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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| 90 | bounds(u{k},sysStruct.umin,sysStruct.umax); |
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| 91 | bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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| 92 | % bounds(t,0,60); |
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| 93 | |
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| 94 | F = F + set(sysStruct.umin < u{k} < sysStruct.umax); |
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| 95 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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| 96 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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| 97 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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| 98 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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| 99 | |
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| 100 | F = F + set(-t < [x{k};u{k}] < t) ; |
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| 101 | |
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| 102 | % PWA Dynamics |
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| 103 | for i = 1:length(sysStruct.A) |
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| 104 | F = F + set(implies(d(i),x{k+1} == sysStruct.A{i}*x{k}+sysStruct.B{i}*u{k}+sysStruct.f{i})); |
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| 105 | |
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| 106 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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| 107 | end |
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| 108 | F = F + set(sum(d) == 1); |
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| 109 | % obj = obj + x{k}'*x{k}+u{k}'*u{k}; |
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| 110 | obj = obj + sum(t); |
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| 111 | end |
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| 112 | [mpsol{k},sol{k},Uz{k}] = solvemp(F,obj,[],x{k},u{k}); |
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| 113 | sol = solvesdp(F+set(x{k}==[1.2;1.1;1.1]),obj) |
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| 114 | |
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| 115 | |
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| 116 | |
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| 117 | |
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