Hello,
I am trying to synthesize an LQR controller solving the problem as linear programming with LMI constraints (using MATLAB function msfsyn). The algorithm works fine only with small values of matrix Q. As soon as I increase the state weight (in matrix Q) MATLAB returns the LMI optimization problem is unfeasible. Any suggestion? Is it a numerical problem? Any way to solve it?
Attached the script I am using. For Q(1) = 10 it works fine. For Q(1) = 1e10 the problem is unfeasible.
Thanks.
Andrea
Here works fine with Q = diag([1e10 0 0 0 0]);
Result: feasible solution of required accuracy
best objective value: 3.836320e+08
guaranteed relative accuracy: 9.50e-03.
But, also because of LMI restrictions, the problem of viability of the solution is common. So, you must choose the weight matrix Q such that the problem is feasible.
I run your file for Q = diag([1e10 0 0 0 0]); I got the same objective value and accuracy results of Rosana C. B. Rego. Comparing lqr results, the state feedback vector differs at higher Q values in the LMI computation.
Klqr =
1.0e+04 *
8.5383 0.1485 0.0012 0.0000 0.0000
Klmi =
1.0e+04 *
-4.9253 -0.3414 -0.0105 -0.0002 -0.0000
I can surely recommend the methodology adopted by selim for second equation in klmi =
Klmi =
1.0e+04 *
-4.9253 -0.3414 -0.0105 -0.0002 -0.0000
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