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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