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 | B1 = [1;0]; |
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7 | B2 = pi*B1; |
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8 | nu = 1; |
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9 | C = [0.5 0.5]; |
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10 | |
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11 | % Prediction horizon |
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12 | N = 4; |
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13 | |
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14 | % States x(k), ..., x(k+N) |
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15 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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16 | |
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17 | % Inputs u(k), ..., u(k+N) (last one not used) |
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18 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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19 | |
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20 | % Binary for PWA selection |
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21 | d = binvar(repmat(2,1,N),repmat(1,1,N)); |
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22 | |
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23 | % Value functions |
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24 | J = cell(1,N); |
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25 | |
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26 | % Initialize value function at stage N |
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27 | J{N} = 0; |
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28 | |
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29 | % DP iteration from final state |
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30 | for k = N-1:-1:1 |
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31 | |
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32 | % Control constraints |
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33 | F = set(-1 < u{k} < 1); |
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34 | |
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35 | % We are in a feasible region... |
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36 | F = F + set(-1 < C*x{k} < 1); |
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37 | F = F + set(-5 < x{k} < 5); |
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38 | |
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39 | % ...and go to a feasible region |
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40 | F = F + set(-1 < C*x{k+1} < 1); |
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41 | F = F + set(-5 < x{k+1} < 5); |
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42 | |
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43 | % PWA Dynamics |
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44 | F = F + set(implies(d{k}(1),[x{k+1} == A*x{k}+B1*u{k}, x{k}(1) > 0])); |
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45 | F = F + set(implies(d{k}(2),[x{k+1} == A*x{k}+B2*u{k}, x{k}(1) < 0])); |
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46 | F = F + set(sum(d{k}) == 1); |
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47 | |
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48 | % L1 objective |
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49 | obj = norm(x{k},1) + norm(u{k},1); |
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50 | |
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51 | [mpsol{k},sol{k},aux{k},J{k},U{k}] = solvemp(F,obj + J{k+1},[],x{k},u{k}); |
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52 | |
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53 | end |
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54 | |
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55 | |
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56 | |
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57 | |
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58 | |
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59 | break |
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60 | |
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61 | |
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62 | |
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63 | break |
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64 | mpsol{1} = mpt_removeOverlaps(mpsol{1}) |
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65 | |
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66 | % Compare |
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67 | sysStruct.A{1} = A; |
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68 | sysStruct.B{1} = B1; |
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69 | sysStruct.C{1} = C; |
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70 | sysStruct.D{1} = [0]; |
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71 | sysStruct.A{2} = A; |
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72 | sysStruct.B{2} = B2; |
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73 | sysStruct.C{2} = C; |
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74 | sysStruct.D{2} = [0]; |
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75 | sysStruct.guardX{1} = [-1 0]; |
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76 | sysStruct.guardU{1} = [0]; |
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77 | sysStruct.guardC{1} = [0]; |
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78 | sysStruct.guardX{2} = [1 0]; |
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79 | sysStruct.guardU{2} = [0]; |
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80 | sysStruct.guardC{2} = [0]; |
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81 | |
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82 | %set constraints on output |
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83 | sysStruct.ymin = -1; |
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84 | sysStruct.ymax = 1; |
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85 | |
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86 | %set constraints on input |
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87 | sysStruct.umin = -1; |
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88 | sysStruct.umax = 1; |
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89 | |
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90 | sysStruct.xmin = [-5;-5]; |
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91 | sysStruct.xmax = [5;5]; |
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92 | |
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93 | probStruct.norm=1; |
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94 | probStruct.Q=eye(2); |
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95 | probStruct.R=1; |
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96 | probStruct.N=N-1; |
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97 | probStruct.P_N=zeros(2); |
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98 | probStruct.subopt_lev=0; |
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99 | probStruct.y0bounds=1; |
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100 | probStruct.Tconstraint=0; |
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101 | ctrl=mpt_control(sysStruct,probStruct) |
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102 | |
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103 | mpt_isPWAbigger(ctrl,mpsol{1}) |
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104 | break |
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105 | %[ii,jj] = isinside(ctrl.Pn,[1.2;0.8]); |
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106 | %ctrl.Bi{jj}*[1.2;0.8]+ctrl.Ci{jj} |
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107 | |
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108 | % |
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109 | % |
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110 | % Online |
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111 | obj = 0; |
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112 | F = set([]); |
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113 | dd = []; |
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114 | for k = N-1:-1:1 |
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115 | |
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116 | % Feasible region |
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117 | F = F + set(-1 < u{k} < 1); |
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118 | F = F + set(-1 < C*x{k} < 1); |
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119 | F = F + set(-5 < x{k} < 5); |
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120 | F = F + set(-1 < C*x{k+1} < 1); |
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121 | F = F + set(-5 < x{k+1} < 5); |
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122 | |
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123 | % PWA Dynamics |
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124 | d = binvar(2,1);dd = [dd;d]; |
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125 | F = F + set(implies(d(1),x{k+1} == (A*x{k}+B1*u{k}))); |
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126 | F = F + set(implies(d(2),x{k+1} == (A*x{k}+B2*u{k}))); |
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127 | F = F + set(implies(d(1),x{k}(1) > 0)); |
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128 | F = F + set(implies(d(2),x{k}(1) < 0)); |
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129 | F = F + set(sum(d) == 1); |
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130 | |
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131 | F1 = set(x{k+1} == (A*x{k}+B1*u{k})) + set(x{k}(1) > 0); |
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132 | F2 = set(x{k+1} == (A*x{k}+B2*u{k})) + set(x{k}(1) < 0); |
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133 | |
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134 | %F = F + hull(F1,F2); |
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135 | |
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136 | % obj = obj + norm([x{k};u{k}],1); |
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137 | obj = obj + norm([x{k};u{k}],1); |
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138 | % obj = obj + norm([x{k};u{k}],1); |
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139 | % Compute value function for one step backwards |
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140 | end |
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141 | mpsol2{k} = solvemp(F,obj,[],x{k},u{k}); |
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142 | mpsol3{k} = dua_test(F,obj,[],x{k}); |
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143 | solvesdp(F+set(x{k}==[0.5;0.5]),obj) |
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144 | solvesdp(F+set(x{k}==[1.2;0.8]),obj) |
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145 | mpsol{k} = solvemp(F,obj,[],x{k},u); |
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146 | mpsol2{1} = rmovlps(mpsol2{1}); |
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147 | |
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148 | mpsol1{k} = solvemp(F,obj,[],x{k},u{k}); |
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149 | % |
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