[37] | 1 | yalmip('clear') |
---|
| 2 | clear all |
---|
| 3 | |
---|
| 4 | % Data |
---|
| 5 | A = [2 -1;1 0];nx = 2; |
---|
| 6 | B = [1;0];nu = 1; |
---|
| 7 | C = [0.5 0.5]; |
---|
| 8 | |
---|
| 9 | % Prediction horizon |
---|
| 10 | N = 4; |
---|
| 11 | |
---|
| 12 | % Future state |
---|
| 13 | % Now for two different noises |
---|
| 14 | x1 = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
---|
| 15 | x2 = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
---|
| 16 | |
---|
| 17 | % Current state |
---|
| 18 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
---|
| 19 | |
---|
| 20 | % Inputs u(k), ..., u(k+N) (last one not used) |
---|
| 21 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
---|
| 22 | |
---|
| 23 | % Binary for PWA selection |
---|
| 24 | d = binvar(2,1); |
---|
| 25 | |
---|
| 26 | % Value functions |
---|
| 27 | J = cell(1,N); |
---|
| 28 | |
---|
| 29 | % Initialize value function at stage N |
---|
| 30 | |
---|
| 31 | J{N} = 0; |
---|
| 32 | J1{N} = pwa(norm(x1{N},1),set(-10<x1{N}(1)<10)); |
---|
| 33 | J2{N} = pwa(norm(x2{N},1),set(-10<x2{N}(1)<10)); |
---|
| 34 | |
---|
| 35 | |
---|
| 36 | t = sdpvar(nx+nu,1); |
---|
| 37 | bounds(t,0,600); |
---|
| 38 | for k = N-1:-1:1 |
---|
| 39 | |
---|
| 40 | bounds(x{k},-5,5); |
---|
| 41 | bounds(u{k},-1,1); |
---|
| 42 | bounds(x1{k+1},-5,5); |
---|
| 43 | bounds(x2{k+1},-5,5); |
---|
| 44 | |
---|
| 45 | % Feasible region |
---|
| 46 | F = set(-1 < u{k} < 1); |
---|
| 47 | F = F + set(-1 < C*x{k} < 1); |
---|
| 48 | F = F + set(-5 < x{k} < 5); |
---|
| 49 | |
---|
| 50 | F = F + set(-1 < C*x1{k+1} < 1); |
---|
| 51 | F = F + set(-1 < C*x2{k+1} < 1); |
---|
| 52 | F = F + set(-5 < x1{k} < 5); |
---|
| 53 | F = F + set(-5 < x2{k} < 5); |
---|
| 54 | |
---|
| 55 | % PWA Dynamics, noise 1 |
---|
| 56 | F = F + set(implies(d(1),x1{k+1} == (A*x{k}+B*u{k}+[-0.001;0]))); |
---|
| 57 | F = F + set(implies(d(2),x1{k+1} == (A*x{k}+pi*B*u{k}+[-0.001;0]))); |
---|
| 58 | |
---|
| 59 | % PWA Dynamics, noise 2 |
---|
| 60 | F = F + set(implies(d(1),x2{k+1} == (A*x{k}+B*u{k}+[0.001;0]))); |
---|
| 61 | F = F + set(implies(d(2),x2{k+1} == (A*x{k}+pi*B*u{k}+[0.001;0]))); |
---|
| 62 | |
---|
| 63 | % Region switcher |
---|
| 64 | F = F + set(implies(d(1),x{k}(1) > 0)); |
---|
| 65 | F = F + set(implies(d(2),x{k}(1) < 0)); |
---|
| 66 | F = F + set(sum(d) == 1); |
---|
| 67 | |
---|
| 68 | F = F + set(-t < [x{k};u{k}] < t) ; |
---|
| 69 | |
---|
| 70 | if k<N-1 |
---|
| 71 | % Create two value functions, minimize worst case |
---|
| 72 | J1{k+1} = pwf(mpsol{k+1},x1{k+1},'convexoverlapping'); |
---|
| 73 | J2{k+1} = pwf(mpsol{k+1},x2{k+1},'convexoverlapping'); |
---|
| 74 | sdpvar v |
---|
| 75 | F = F + set(J1{k+1} < v) + set(J2{k+1} < v); |
---|
| 76 | obj = sum(t) + v; |
---|
| 77 | else |
---|
| 78 | %J1{N} = 0; |
---|
| 79 | %J2{N} = 0; |
---|
| 80 | sdpvar v |
---|
| 81 | F = F + set(J1{k+1} < v) + set(J2{k+1} < v); |
---|
| 82 | obj = sum(t)+v; |
---|
| 83 | end |
---|
| 84 | [mpsol{k},sol{k},Uz{k},J{k}] = solvemp(F,obj,[],x{k},u{k}); |
---|
| 85 | end |
---|
| 86 | |
---|
| 87 | |
---|
| 88 | mpsol{k} = rmovlps(mpsol{k}) |
---|
| 89 | |
---|
| 90 | break |
---|
| 91 | |
---|
| 92 | |
---|
| 93 | % Compare |
---|
| 94 | sysStruct.A{1} = A; |
---|
| 95 | sysStruct.B{1} = B; |
---|
| 96 | sysStruct.C{1} = C; |
---|
| 97 | sysStruct.D{1} = [0]; |
---|
| 98 | sysStruct.A{2} = A; |
---|
| 99 | sysStruct.B{2} = B*pi; |
---|
| 100 | sysStruct.C{2} = C; |
---|
| 101 | sysStruct.D{2} = [0]; |
---|
| 102 | sysStruct.guardX{1} = [-1 0]; |
---|
| 103 | sysStruct.guardU{1} = [0]; |
---|
| 104 | sysStruct.guardC{1} = [0]; |
---|
| 105 | sysStruct.guardX{2} = [1 0]; |
---|
| 106 | sysStruct.guardU{2} = [0]; |
---|
| 107 | sysStruct.guardC{2} = [0]; |
---|
| 108 | |
---|
| 109 | %set constraints on output |
---|
| 110 | sysStruct.ymin = -1; |
---|
| 111 | sysStruct.ymax = 1; |
---|
| 112 | |
---|
| 113 | %set constraints on input |
---|
| 114 | sysStruct.umin = -1; |
---|
| 115 | sysStruct.umax = 1; |
---|
| 116 | |
---|
| 117 | sysStruct.xmin = [-5;-5]; |
---|
| 118 | sysStruct.xmax = [5;5]; |
---|
| 119 | |
---|
| 120 | probStruct.norm=1; |
---|
| 121 | probStruct.Q=eye(2); |
---|
| 122 | probStruct.R=1; |
---|
| 123 | probStruct.N=N-1; |
---|
| 124 | probStruct.P_N=zeros(2); |
---|
| 125 | probStruct.subopt_lev=0; |
---|
| 126 | probStruct.y0bounds=1; |
---|
| 127 | probStruct.Tconstraint=0; |
---|
| 128 | ctrl=mpt_control(sysStruct,probStruct) |
---|
| 129 | |
---|
| 130 | mpt_isPWAbigger(ctrl,mpsol{1}) |
---|
| 131 | break |
---|
| 132 | %[ii,jj] = isinside(ctrl.Pn,[1.2;0.8]); |
---|
| 133 | %ctrl.Bi{jj}*[1.2;0.8]+ctrl.Ci{jj} |
---|
| 134 | |
---|
| 135 | % |
---|
| 136 | % |
---|
| 137 | % % Online |
---|
| 138 | % obj = 0; |
---|
| 139 | % F = set([]); |
---|
| 140 | % dd = []; |
---|
| 141 | % for k = N-1:-1:1 |
---|
| 142 | % |
---|
| 143 | % bounds(x{k},-5,5); |
---|
| 144 | % bounds(u{k},-1,1); |
---|
| 145 | % bounds(x{k+1},-5,5); |
---|
| 146 | % |
---|
| 147 | % % Feasible region |
---|
| 148 | % F = F + set(-1 < u{k} < 1); |
---|
| 149 | % F = F + set(-1 < C*x{k} < 1); |
---|
| 150 | % F = F + set(-5 < x{k} < 5); |
---|
| 151 | % F = F + set(-1 < C*x{k+1} < 1); |
---|
| 152 | % F = F + set(-5 < x{k+1} < 5); |
---|
| 153 | % |
---|
| 154 | % % PWA Dynamics |
---|
| 155 | % d = binvar(2,1);dd = [dd;d]; |
---|
| 156 | % F = F + set(implies(d(1),x{k+1} == (A*x{k}+B*u{k}))); |
---|
| 157 | % F = F + set(implies(d(2),x{k+1} == (A*x{k}+pi*B*u{k}))); |
---|
| 158 | % F = F + set(implies(d(1),x{k}(1) > 0)); |
---|
| 159 | % F = F + set(implies(d(2),x{k}(1) < 0)); |
---|
| 160 | % F = F + set(sum(d) == 1); |
---|
| 161 | % % F = F + set(-0.1 < u{k}-u{k+1} < 0.1); |
---|
| 162 | % obj = obj + norm([x{k};u{k}],1); |
---|
| 163 | % %obj = obj + x{k}'*x{k}+u{k}'*u{k};%norm([x{k};u{k}],1); |
---|
| 164 | % % Compute value function for one step backwards |
---|
| 165 | % end |
---|
| 166 | % [mpsol2{k},sol{k},Uz{k},J2{k},U{k}] = solvemp(F,obj,[],x{k},u{k}); |
---|
| 167 | % solvesdp(F+set(x{k}==[0.5;0.5]),obj) |
---|
| 168 | % solvesdp(F+set(x{k}==[1.2;0.8]),obj) |
---|
| 169 | % mpsol{k} = solvemp(F,obj,[],x{k},u); |
---|
| 170 | % mpsol{1} = rmovlps(mpsol{1}); |
---|
| 171 | % |
---|
| 172 | % |
---|