1 | yalmip('clear') |
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2 | %clear all |
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3 | |
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4 | % Data |
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5 | A = [2 -1;1 0];nx = 2; |
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6 | B = [1;0];nu = 1; |
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7 | C = [0.5 0.5]; |
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8 | |
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9 | % Prediction horizon |
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10 | N = 3; |
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11 | |
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12 | % States x(k), ..., x(k+N) |
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13 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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14 | |
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15 | % Inputs u(k), ..., u(k+N) (last one not used) |
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16 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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17 | |
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18 | % Value functions |
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19 | J = cell(1,N); |
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20 | |
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21 | % Initialize value function at stage N |
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22 | J{N} = 0; |
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23 | U{N} = 0; |
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24 | for k = N-1:-1:1 |
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25 | |
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26 | % Feasible region |
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27 | bounds(x{k},-5,5); |
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28 | bounds(u{k},-1,1); |
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29 | bounds(x{k+1},-5,5); |
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30 | |
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31 | F = set(-1 < u{k} < 1); |
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32 | F = F + set(-1 < C*x{k} < 1); |
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33 | F = F + set(-5 < x{k} < 5); |
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34 | F = F + set(-1 < C*x{k+1} < 1); |
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35 | F = F + set(-5 < x{k+1} < 5); |
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36 | |
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37 | % LTI Dynamics |
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38 | F = F + set(x{k+1} == A*x{k}+B*u{k}); |
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39 | |
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40 | obj = norm(x{k},inf) + norm(u{k},inf); |
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41 | |
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42 | % Compute value function for one step backwards |
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43 | % [mpsol{k},sol{k},Uz{k},J{k},U{k}] = solvemp(F,max(obj,J{k+1}),[],x{k},u{k}); |
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44 | [mpsol{k},sol{k},Uz{k},J{k},U{k}] = solvemp(F,obj+J{k+1},[],x{k},u{k}); |
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45 | end |
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46 | |
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47 | |
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48 | % MPT implementation |
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49 | sysStruct.A= A; |
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50 | sysStruct.B= B; |
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51 | sysStruct.C= C; |
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52 | sysStruct.D= [0]; |
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53 | |
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54 | %set constraints on output |
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55 | sysStruct.ymin = -1; |
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56 | sysStruct.ymax = 1; |
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57 | |
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58 | %set constraints on input |
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59 | sysStruct.umin = -1; |
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60 | sysStruct.umax = 1; |
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61 | |
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62 | sysStruct.xmin = [-5;-5]; |
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63 | sysStruct.xmax = [5;5]; |
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64 | |
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65 | probStruct.norm=inf; |
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66 | probStruct.Q=eye(2); |
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67 | probStruct.R=1; |
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68 | probStruct.N=N-1; |
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69 | probStruct.P_N=zeros(2); |
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70 | probStruct.subopt_lev=0; |
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71 | probStruct.y0bounds=1; |
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72 | probStruct.Tconstraint=0; |
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73 | ctrl=mpt_control(sysStruct,probStruct) |
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74 | mpt_isPWAbigger(mpsol{1}{1},ctrl) |
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75 | |
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76 | |
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77 | |
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78 | |
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79 | |
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80 | break |
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81 | |
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82 | |
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83 | |
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84 | |
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85 | |
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86 | % Prediction horizon |
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87 | N = 5; |
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88 | |
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89 | % States x(k), ..., x(k+N) |
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90 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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91 | |
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92 | % Inputs u(k), ..., u(k+N) (last one not used) |
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93 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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94 | |
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95 | % Value functions |
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96 | J = cell(1,N); |
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97 | |
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98 | % Initialize value function at stage N |
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99 | J{N} = 0; |
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100 | F = set([]); |
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101 | obj = 0; |
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102 | for k = N-1:-1:1 |
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103 | % Feasible region |
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104 | F = F + set(-1 < u{k} < 1); |
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105 | F = F + set(-1 < C*x{k} < 1); |
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106 | F = F + set(-5 < x{k} < 5); |
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107 | F = F + set(-1 < C*x{k+1} < 1); |
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108 | F = F + set(-5 < x{k+1} < 5); |
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109 | |
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110 | % LTI Dynamics |
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111 | F = F + set(x{k+1} == A*x{k}+B*u{k}); |
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112 | |
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113 | % Compute value function for one step backwards |
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114 | obj = max(obj,norm([x{k};u{k}],inf)); |
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115 | |
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116 | end |
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117 | %F = F + set(norm(x{k+1},1) < norm(x{k},1)) |
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118 | solvesdp(F+set(x{1}==[0.5;-1]),obj) |
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119 | |
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120 | [mpsol{k},xx,cc,vv,U{k}] = solvemp(F,obj,[],x{k},u{k}); |
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121 | |
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122 | |
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123 | |
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124 | |
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125 | assign(x{k},[-0.5;-1]); |
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126 | xx = [-0.5;-1]; |
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127 | for i = 1:10 |
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128 | xx = A*xx + B*double(U{k}) |
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129 | assign(x{k},xx); |
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130 | double(x{k}) |
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131 | plot(xx(1),xx(2),'*k');drawnow |
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132 | end |
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133 | |
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134 | |
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135 | |
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136 | |
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