[37] | 1 | function dplti_1 |
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| 2 | |
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| 3 | % Data |
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| 4 | A = [2 -1;1 0];nx = 2; |
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| 5 | B = [1;0];nu = 1; |
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| 6 | C = [0.5 0.5]; |
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| 7 | |
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| 8 | % Prediction horizon |
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| 9 | N = 5; |
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| 10 | |
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| 11 | % States x(k), ..., x(k+N) |
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| 12 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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| 13 | |
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| 14 | % Inputs u(k), ..., u(k+N) (last one not used) |
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| 15 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 16 | |
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| 17 | % MPT implementation |
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| 18 | sysStruct.A= A; |
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| 19 | sysStruct.B= B; |
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| 20 | sysStruct.C= C; |
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| 21 | sysStruct.D= [0]; |
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| 22 | |
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| 23 | %set constraints on output |
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| 24 | sysStruct.ymin = -1; |
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| 25 | sysStruct.ymax = 1; |
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| 26 | |
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| 27 | %set constraints on input |
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| 28 | sysStruct.umin = -1; |
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| 29 | sysStruct.umax = 1; |
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| 30 | |
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| 31 | sysStruct.xmin = [-5;-5]; |
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| 32 | sysStruct.xmax = [5;5]; |
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| 33 | |
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| 34 | probStruct.norm=1; |
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| 35 | probStruct.Q=eye(2); |
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| 36 | probStruct.R=1; |
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| 37 | probStruct.N=N-1; |
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| 38 | probStruct.P_N=zeros(2); |
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| 39 | probStruct.subopt_lev=0; |
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| 40 | probStruct.y0bounds=1; |
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| 41 | probStruct.Tconstraint=0; |
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| 42 | ctrl=mpt_control(sysStruct,probStruct) |
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| 43 | |
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| 44 | % States x(k), ..., x(k+N) |
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| 45 | x = sdpvar(repmat(nx,1,N),repmat(1,1,N)); |
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| 46 | |
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| 47 | % Inputs u(k), ..., u(k+N) (last one not used) |
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| 48 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 49 | |
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| 50 | % Value functions |
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| 51 | J = cell(1,N); |
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| 52 | |
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| 53 | % Initialize value function at stage N |
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| 54 | J{N} = 0; |
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| 55 | F = set([]); |
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| 56 | obj = 0; |
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| 57 | for k = N-1:-1:1 |
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| 58 | % Feasible region |
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| 59 | F = F + set(-1 < u{k} < 1); |
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| 60 | F = F + set(-1 < C*x{k} < 1); |
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| 61 | F = F + set(-5 < x{k} < 5); |
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| 62 | F = F + set(-1 < C*x{k+1} < 1); |
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| 63 | F = F + set(-5 < x{k+1} < 5); |
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| 64 | |
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| 65 | % LTI Dynamics |
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| 66 | F = F + set(x{k+1} == A*x{k}+B*u{k}); |
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| 67 | |
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| 68 | % Compute value function for one step backwards |
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| 69 | obj = obj + norm([x{k};u{k}],1); |
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| 70 | end |
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| 71 | mpsol{1} = solvemp(F,obj,[],x{k},u{k}); |
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| 72 | |
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| 73 | mbg_asserttolequal(mpt_isPWAbigger(mpsol{1}{1},ctrl),0); |
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| 74 | |
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| 75 | |
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| 78 | |
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