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[37] | 1 | function test_robust_2 |
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| 2 | |
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| 3 | yalmip('clear') |
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| 4 | |
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| 5 | Anominal = [0 1 0;0 0 1;0 0 0]; |
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| 6 | B = [0;0;1]; |
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| 7 | Q = eye(3) |
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| 8 | R = 1; |
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| 9 | |
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| 10 | alpha = sdpvar(1) |
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| 11 | A = double2sdpvar(Anominal); |
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| 12 | A(1,3) = alpha; |
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| 13 | |
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| 14 | %We have now created a parameterized system, and can proceed as before. |
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| 15 | Y = sdpvar(3,3); |
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| 16 | L = sdpvar(1,3); |
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| 17 | |
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| 18 | F = set(Y >=0); |
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| 19 | F = F + set([-A*Y-B*L + (-A*Y-B*L)' Y L';Y inv(Q) zeros(3,1);L zeros(1,3) inv(R)] > 0) |
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| 20 | |
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| 21 | F = F + set(-0.1 <= alpha <= 0.1); |
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| 22 | |
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| 23 | sol = solverobust(F,-trace(Y),[],alpha) |
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| 24 | |
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| 25 | K = double(L)*inv(double(Y)) |
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| 26 | |
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| 27 | mbg_asserttolequal(sol.problem, 0, 1e-5); |
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| 28 | mbg_asserttolequal(K - [-1.3674 -2.9158 -2.6670], 0, 1e-3); |
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| 29 | |
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| 30 | |
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| 31 | alpha = sdpvar(1) |
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| 32 | A = double2sdpvar(Anominal); |
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| 33 | A(1,3) = alpha; |
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| 34 | |
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| 35 | L0 = sdpvar(1,3); |
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| 36 | L1 = sdpvar(1,3); |
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| 37 | L = L0 + alpha*L1; |
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| 38 | |
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| 39 | Y0 = sdpvar(3,3); |
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| 40 | Y1 = sdpvar(3,3); |
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| 41 | Y = Y0 + alpha*Y1; |
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| 42 | |
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| 43 | F = set(Y >=0); |
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| 44 | F = F + set([-A*Y-B*L + (-A*Y-B*L)' Y L';Y inv(Q) zeros(3,1);L zeros(1,3) inv(R)] > 0) |
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| 45 | F = F + set(-0.1 <= alpha <= 0.1); |
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| 46 | sol = solverobust(F,-trace(Y),[],alpha) |
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| 47 | |
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| 48 | mbg_asserttolequal(sol.problem, 0, 1e-5); |
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| 49 | Y0 = double(Y0); |
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| 50 | Y1 = double(Y1); |
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| 51 | mbg_asserttolequal(max([trace(Y0-0.1*trace(Y1)) trace(Y0+0.1*trace(Y1))]),2.3319, 1e-3); |
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