[37] | 1 | function testmpdpqp |
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| 2 | |
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| 3 | yalmip('clear') |
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| 4 | |
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| 5 | % Model data |
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| 6 | A = [2 -1;1 0]; |
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| 7 | B = [1;0]; |
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| 8 | C = [0.5 0.5]; |
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| 9 | nx = 2; % Number of states |
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| 10 | nu = 1; % Number of inputs |
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| 11 | |
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| 12 | % Prediction horizon |
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| 13 | N = 5; |
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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 | % Inputs u(k), ..., u(k+N) (last one not used) u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 17 | u = sdpvar(repmat(nu,1,N),repmat(1,1,N)); |
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| 18 | |
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| 19 | J{N} = 0; |
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| 20 | F = set([]); |
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| 21 | for k = N-1:-1:1 |
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| 22 | |
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| 23 | % Feasible region |
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| 24 | F = set(-1 < u{k} < 1); |
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| 25 | F = F + set(-1 < C*x{k} < 1); |
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| 26 | F = F + set(-5 < x{k} < 5); |
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| 27 | F = F + set(-1 < C*x{k+1} < 1); |
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| 28 | F = F + set(-5 < x{k+1} < 5); |
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| 29 | % Dynamics |
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| 30 | F = F + set(x{k+1} == A*x{k}+B*u{k}); |
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| 31 | % Cost in value iteration |
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| 32 | % obj = obj + x{k}'*x{k} + u{k}'*u{k} |
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| 33 | obj = x{k}'*x{k} + u{k}'*u{k} + J{k+1}; |
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| 34 | % Solve one-step problem |
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| 35 | [sol{k},diagnost{k},Uz{k},J{k},Optimizer{k}] = solvemp(F,obj,sdpsettings('solver','mpt'),x{k},u{k}); |
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| 36 | end |
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| 37 | |
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| 38 | assign(x{k},[1;0.5]) |
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| 39 | mbg_asserttrue(diagnost{1}.problem == 0); |
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| 40 | mbg_asserttolequal(double(J{k}),3.82456140350877,1e-5); |
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| 41 | mbg_asserttolequal(double(Optimizer{k}),-1,1e-5); |
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| 42 | |
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| 43 | assign(x{k},[0.5;1]) |
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| 44 | mbg_asserttolequal(double(J{k}), 1.6140350,1e-5); |
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| 45 | |
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| 46 | assign(x{k},[0;1.9]) |
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| 47 | mbg_asserttolequal(double(J{k}), 8.755,1e-5); |
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| 48 | |
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| 49 | assign(x{k},[-0.1;-1.85]) |
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| 50 | mbg_asserttolequal(double(J{k}), 6.61825,1e-5); |
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| 51 | |
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| 52 | |
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