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 = 4; |
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11 | |
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12 | % Future state |
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13 | % Now for two different noises |
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14 | x1 = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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15 | x2 = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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16 | |
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17 | % Current state |
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18 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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19 | |
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20 | % Inputs u(k), ..., u(k+N) (last one not used) |
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21 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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22 | |
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23 | % Binary for PWA selection |
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24 | d = binvar(2,1); |
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25 | |
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26 | % Value functions |
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27 | J = cell(1,N); |
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28 | |
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29 | % Initialize value function at stage N |
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30 | |
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31 | J{N} = 0; |
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32 | J1{N} = pwa(norm(x1{N},1),set(-10<x1{N}(1)<10)); |
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33 | J2{N} = pwa(norm(x2{N},1),set(-10<x2{N}(1)<10)); |
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34 | |
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35 | |
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36 | t = sdpvar(nx+nu,1); |
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37 | bounds(t,0,600); |
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38 | for k = N-1:-1:1 |
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39 | |
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40 | bounds(x{k},-5,5); |
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41 | bounds(u{k},-1,1); |
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42 | bounds(x1{k+1},-5,5); |
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43 | bounds(x2{k+1},-5,5); |
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44 | |
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45 | % Feasible region |
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46 | F = set(-1 < u{k} < 1); |
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47 | F = F + set(-1 < C*x{k} < 1); |
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48 | F = F + set(-5 < x{k} < 5); |
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49 | |
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50 | F = F + set(-1 < C*x1{k+1} < 1); |
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51 | F = F + set(-1 < C*x2{k+1} < 1); |
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52 | F = F + set(-5 < x1{k} < 5); |
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53 | F = F + set(-5 < x2{k} < 5); |
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54 | |
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55 | % PWA Dynamics, noise 1 |
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56 | F = F + set(implies(d(1),x1{k+1} == (A*x{k}+B*u{k}+[-0.001;0]))); |
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57 | F = F + set(implies(d(2),x1{k+1} == (A*x{k}+pi*B*u{k}+[-0.001;0]))); |
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58 | |
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59 | % PWA Dynamics, noise 2 |
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60 | F = F + set(implies(d(1),x2{k+1} == (A*x{k}+B*u{k}+[0.001;0]))); |
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61 | F = F + set(implies(d(2),x2{k+1} == (A*x{k}+pi*B*u{k}+[0.001;0]))); |
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62 | |
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63 | % Region switcher |
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64 | F = F + set(implies(d(1),x{k}(1) > 0)); |
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65 | F = F + set(implies(d(2),x{k}(1) < 0)); |
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66 | F = F + set(sum(d) == 1); |
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67 | |
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68 | F = F + set(-t < [x{k};u{k}] < t) ; |
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69 | |
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70 | if k<N-1 |
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71 | % Create two value functions, minimize worst case |
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72 | J1{k+1} = pwf(mpsol{k+1},x1{k+1},'convexoverlapping'); |
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73 | J2{k+1} = pwf(mpsol{k+1},x2{k+1},'convexoverlapping'); |
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74 | sdpvar v |
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75 | F = F + set(J1{k+1} < v) + set(J2{k+1} < v); |
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76 | obj = sum(t) + v; |
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77 | else |
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78 | %J1{N} = 0; |
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79 | %J2{N} = 0; |
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80 | sdpvar v |
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81 | F = F + set(J1{k+1} < v) + set(J2{k+1} < v); |
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82 | obj = sum(t)+v; |
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83 | end |
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84 | [mpsol{k},sol{k},Uz{k},J{k}] = solvemp(F,obj,[],x{k},u{k}); |
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85 | end |
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86 | |
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87 | |
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88 | mpsol{k} = rmovlps(mpsol{k}) |
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89 | |
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90 | break |
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91 | |
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92 | |
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93 | % Compare |
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94 | sysStruct.A{1} = A; |
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95 | sysStruct.B{1} = B; |
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96 | sysStruct.C{1} = C; |
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97 | sysStruct.D{1} = [0]; |
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98 | sysStruct.A{2} = A; |
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99 | sysStruct.B{2} = B*pi; |
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100 | sysStruct.C{2} = C; |
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101 | sysStruct.D{2} = [0]; |
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102 | sysStruct.guardX{1} = [-1 0]; |
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103 | sysStruct.guardU{1} = [0]; |
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104 | sysStruct.guardC{1} = [0]; |
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105 | sysStruct.guardX{2} = [1 0]; |
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106 | sysStruct.guardU{2} = [0]; |
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107 | sysStruct.guardC{2} = [0]; |
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108 | |
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109 | %set constraints on output |
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110 | sysStruct.ymin = -1; |
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111 | sysStruct.ymax = 1; |
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112 | |
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113 | %set constraints on input |
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114 | sysStruct.umin = -1; |
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115 | sysStruct.umax = 1; |
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116 | |
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117 | sysStruct.xmin = [-5;-5]; |
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118 | sysStruct.xmax = [5;5]; |
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119 | |
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120 | probStruct.norm=1; |
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121 | probStruct.Q=eye(2); |
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122 | probStruct.R=1; |
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123 | probStruct.N=N-1; |
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124 | probStruct.P_N=zeros(2); |
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125 | probStruct.subopt_lev=0; |
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126 | probStruct.y0bounds=1; |
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127 | probStruct.Tconstraint=0; |
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128 | ctrl=mpt_control(sysStruct,probStruct) |
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129 | |
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130 | mpt_isPWAbigger(ctrl,mpsol{1}) |
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131 | break |
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132 | %[ii,jj] = isinside(ctrl.Pn,[1.2;0.8]); |
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133 | %ctrl.Bi{jj}*[1.2;0.8]+ctrl.Ci{jj} |
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134 | |
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135 | % |
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136 | % |
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137 | % % Online |
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138 | % obj = 0; |
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139 | % F = set([]); |
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140 | % dd = []; |
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141 | % for k = N-1:-1:1 |
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142 | % |
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143 | % bounds(x{k},-5,5); |
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144 | % bounds(u{k},-1,1); |
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145 | % bounds(x{k+1},-5,5); |
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146 | % |
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147 | % % Feasible region |
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148 | % F = F + set(-1 < u{k} < 1); |
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149 | % F = F + set(-1 < C*x{k} < 1); |
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150 | % F = F + set(-5 < x{k} < 5); |
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151 | % F = F + set(-1 < C*x{k+1} < 1); |
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152 | % F = F + set(-5 < x{k+1} < 5); |
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153 | % |
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154 | % % PWA Dynamics |
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155 | % d = binvar(2,1);dd = [dd;d]; |
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156 | % F = F + set(implies(d(1),x{k+1} == (A*x{k}+B*u{k}))); |
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157 | % F = F + set(implies(d(2),x{k+1} == (A*x{k}+pi*B*u{k}))); |
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158 | % F = F + set(implies(d(1),x{k}(1) > 0)); |
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159 | % F = F + set(implies(d(2),x{k}(1) < 0)); |
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160 | % F = F + set(sum(d) == 1); |
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161 | % % F = F + set(-0.1 < u{k}-u{k+1} < 0.1); |
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162 | % obj = obj + norm([x{k};u{k}],1); |
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163 | % %obj = obj + x{k}'*x{k}+u{k}'*u{k};%norm([x{k};u{k}],1); |
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164 | % % Compute value function for one step backwards |
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165 | % end |
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166 | % [mpsol2{k},sol{k},Uz{k},J2{k},U{k}] = solvemp(F,obj,[],x{k},u{k}); |
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167 | % solvesdp(F+set(x{k}==[0.5;0.5]),obj) |
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168 | % solvesdp(F+set(x{k}==[1.2;0.8]),obj) |
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169 | % mpsol{k} = solvemp(F,obj,[],x{k},u); |
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170 | % mpsol{1} = rmovlps(mpsol{1}); |
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171 | % |
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172 | % |
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