1 | yalmip('clear') |
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2 | mpt_init('lpsolver','clp') |
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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 | pwa3d |
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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.N=N-1; |
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12 | probStruct.norm = 1; |
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13 | probStruct.subopt_lev=0; |
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14 | probStruct.P_N = zeros(3); |
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15 | if 0 |
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16 | ctrl=mpt_control(sysStruct,probStruct) |
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17 | end |
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18 | nx = 3; |
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19 | nu = 1; |
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20 | |
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21 | % States x(k), ..., x(k+N) |
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22 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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23 | |
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24 | % Inputs u(k), ..., u(k+N) (last one not used) |
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25 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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26 | |
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27 | % Binary for PWA selection |
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28 | d = binvar(2,1); |
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29 | |
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30 | % Value functions |
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31 | J = cell(1,N); |
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32 | |
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33 | tic |
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34 | % Initialize value function at stage N |
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35 | J{N} = 0; |
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36 | sysStruct.xmin = sysStruct.ymin; |
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37 | sysStruct.xmax = sysStruct.ymax; |
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38 | for k = N-1:-1:1 |
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39 | % Feasible region |
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40 | t = sdpvar(nx+nu,1); |
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41 | % bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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42 | % bounds(u{k},sysStruct.umin,sysStruct.umax); |
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43 | % bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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44 | % bounds(t,0,600); |
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45 | |
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46 | F = set(sysStruct.umin < u{k} < sysStruct.umax); |
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47 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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48 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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49 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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50 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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51 | |
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52 | F = F + set(-t < [x{k};u{k}] < t) ; |
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53 | F = F + set(0 < t < 600); |
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54 | % PWA Dynamics |
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55 | for i = 1:length(sysStruct.A) |
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56 | 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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57 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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58 | end |
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59 | F = F + set(sum(d) == 1); |
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60 | |
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61 | % Compute value function for one step backwards |
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62 | [mpsol{k},sol{k},Uz{k},J{k}] = solvemp(F,sum(t) + J{k+1},[],x{k},u{k}); |
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63 | end |
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64 | toc |
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65 | break |
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66 | |
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67 | mpsol{1} = mpt_removeOverlaps(mpsol{1}) |
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68 | |
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69 | [pass,tol] = mpt_isPWAbigger(mpsol{1},ctrl) |
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70 | |
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71 | |
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72 | |
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73 | break |
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74 | |
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75 | % On-line solution |
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76 | nx = 3; |
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77 | nu = 1; |
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78 | J{N} = 0; |
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79 | sysStruct.xmin = sysStruct.ymin; |
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80 | sysStruct.xmax = sysStruct.ymax; |
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81 | F = set([]); |
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82 | obj = 0; |
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83 | dd = []; |
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84 | for k = N-1:-1:1 |
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85 | % Feasible region |
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86 | % t = sdpvar(nx+nu,1); |
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87 | d = binvar(2,1);dd = [dd;d]; |
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88 | % obj = obj + sum(t); |
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89 | bounds(x{k},sysStruct.xmin,sysStruct.xmax); |
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90 | bounds(u{k},sysStruct.umin,sysStruct.umax); |
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91 | bounds(x{k+1},sysStruct.xmin,sysStruct.ymax); |
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92 | % bounds(t,0,60); |
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93 | |
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94 | F = F + set(sysStruct.umin < u{k} < sysStruct.umax); |
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95 | F = F + set(sysStruct.xmin < x{k} < sysStruct.xmax); |
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96 | F = F + set(sysStruct.xmin < x{k+1} < sysStruct.xmax); |
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97 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k} < sysStruct.ymax); |
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98 | F = F + set(sysStruct.ymin < sysStruct.C{1}*x{k+1} < sysStruct.ymax); |
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99 | |
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100 | F = F + set(-t < [x{k};u{k}] < t) ; |
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101 | |
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102 | % PWA Dynamics |
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103 | for i = 1:length(sysStruct.A) |
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104 | 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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105 | |
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106 | F = F + set(implies(d(i),sysStruct.guardX{i}*x{k} <= sysStruct.guardC{i})); |
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107 | end |
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108 | F = F + set(sum(d) == 1); |
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109 | % obj = obj + x{k}'*x{k}+u{k}'*u{k}; |
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110 | obj = obj + sum(t); |
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111 | end |
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112 | [mpsol{k},sol{k},Uz{k}] = solvemp(F,obj,[],x{k},u{k}); |
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113 | sol = solvesdp(F+set(x{k}==[1.2;1.1;1.1]),obj) |
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114 | |
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115 | |
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116 | |
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117 | |
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