[37] | 1 | yalmip('clear') |
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| 2 | clear all |
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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 | pwa_car |
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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.Q = eye(2); |
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| 12 | probStruct.N=N-1; |
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| 13 | probStruct.norm = 1; |
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| 14 | probStruct.subopt_lev=0; |
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| 15 | probStruct.P_N = zeros(2); |
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| 16 | probStruct.y0bounds = 1; |
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| 17 | |
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| 18 | if 0 |
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| 19 | ctrl=mpt_control(sysStruct,probStruct) |
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| 20 | mpt_plotpwa(ctrl.Pn,ctrl.Bi,ctrl.Ci) |
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| 21 | end |
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| 22 | nx = 2; |
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| 23 | nu = 1; |
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| 24 | |
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| 25 | % States x(k), ..., x(k+N) |
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| 26 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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| 27 | |
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| 28 | % Inputs u(k), ..., u(k+N) (last one not used) |
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| 29 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 30 | |
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| 31 | % Binary for PWA selection |
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| 32 | d = binvar(4,1); |
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| 33 | |
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| 34 | % Value functions |
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| 35 | J = cell(1,N); |
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| 36 | |
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| 37 | % Initialize value function at stage N |
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| 38 | J{N} = 0; |
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| 39 | sysStruct.xmin = sysStruct.ymin; |
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| 40 | sysStruct.xmax = sysStruct.ymax; |
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| 41 | for k = N-1:-1:1 |
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| 42 | % Feasible region |
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| 43 | t = sdpvar(nx+nu,1); |
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| 44 | bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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| 45 | bounds(u{k},sysStruct.umin,sysStruct.umax); |
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| 46 | bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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| 47 | bounds(t,0,40*2+5+1); |
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| 48 | |
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| 49 | F = set(sysStruct.umin < u{k} < sysStruct.umax); |
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| 50 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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| 51 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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| 52 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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| 53 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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| 54 | |
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| 55 | F = F + set(-t < [x{k};u{k}] < t) ; |
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| 56 | |
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| 57 | % PWA Dynamics |
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| 58 | for i = 1:length(sysStruct.A) |
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| 59 | 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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| 60 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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| 61 | end |
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| 62 | F = F + set(sum(d) == 1); |
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| 63 | |
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| 64 | % Compute value function for one step backwards |
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| 65 | [mpsol{k},sol{k},Uz{k},J{k}] = solvemp(F,sum(t) + J{k+1},[],x{k},u{k}); |
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| 66 | end |
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| 67 | break |
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| 68 | mpsol{1} = rmovlps(mpsol{1}) |
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| 69 | |
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| 70 | %[pass,tol] = mpt_isPWAbigger(mpsol{1},ctrl) |
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| 71 | |
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| 72 | |
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| 73 | |
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| 74 | break |
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| 75 | |
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| 76 | % On-line solution |
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| 77 | J{N} = 0; |
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| 78 | sysStruct.xmin = sysStruct.ymin; |
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| 79 | sysStruct.xmax = sysStruct.ymax; |
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| 80 | F = set([]); |
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| 81 | obj = 0; |
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| 82 | nx = 2; |
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| 83 | nu = 1; |
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| 84 | |
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| 85 | % States x(k), ..., x(k+N) |
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| 86 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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| 87 | |
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| 88 | % Inputs u(k), ..., u(k+N) (last one not used) |
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| 89 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 90 | |
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| 91 | % Binary for PWA selection |
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| 92 | d = binvar(4,1); |
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| 93 | for k = N-1:-1:1 |
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| 94 | % Feasible region |
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| 95 | t = sdpvar(nx+nu,1); |
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| 96 | d = binvar(4,1); |
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| 97 | obj = obj + sum(t); |
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| 98 | bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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| 99 | bounds(u{k},sysStruct.umin,sysStruct.umax); |
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| 100 | bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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| 101 | bounds(t,0,600); |
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| 102 | |
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| 103 | F = F + set(sysStruct.umin < u{k} < sysStruct.umax); |
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| 104 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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| 105 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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| 106 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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| 107 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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| 108 | |
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| 109 | F = F + set(-t < [x{k};u{k}] < t) ; |
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| 110 | |
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| 111 | % PWA Dynamics |
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| 112 | for i = 1:length(sysStruct.A) |
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| 113 | 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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| 114 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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| 115 | end |
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| 116 | F = F + set(sum(d) == 1); |
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| 117 | obj = obj + sum(t); |
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| 118 | |
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| 119 | end |
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| 120 | [mpsol{k},sol{k},Uz{k}] = solvemp(F,obj,[],x{k},u{k}); |
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| 121 | sol = solvesdp(F+set(x{k}==[-6;20]),obj) |
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| 122 | |
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| 123 | |
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| 124 | |
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| 125 | |
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