TomSym Optimal Feedback - A tomSym BMI demonstration: Difference between revisions
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Problem type appears to be: bmi | Problem type appears to be: bmi | ||
Time for symbolic processing: 0. | Time for symbolic processing: 0.05479 seconds | ||
Starting numeric solver | Starting numeric solver | ||
===== * * * =================================================================== * * * | ===== * * * =================================================================== * * * | ||
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FuncEv 13 GradEv 13 Iter 13 MinorIter 31 | FuncEv 13 GradEv 13 Iter 13 MinorIter 31 | ||
Elapsed time: 0.002000 sec. | |||
K_opt = | K_opt = | ||
-0.3634 -0.1741 | -0.3634 -0.1741 | ||
</pre> | </pre> | ||
Latest revision as of 09:32, 8 November 2011
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This page is part of the TomSym Manual. See TomSym Manual. |
A sample problem from the PENBMI manual.
LQ optimal feedback
Minimize trace(P) subject to P >= 0 (LMI) (A+B*K)'*P+P*(A+B*K) <= -eye(2)-K'*K (BMI)
% Variables
toms 2x2 symmetric P
toms 1x2 K
% Constants
A = [-1 2;-3 -4];
B = [1;1];
% Constraints
F = { MI( P >= 0 )
MI( (A+B*K)'*P + P'*(A+B*K) <= -eye(2) - K'*K )};
%Solve the problem
solution = ezsolve(trace(P),F,[],'Optimal feedback');
% Evaluate K using the returned solution
K_opt = subs(K,solution)Problem type appears to be: bmi
Time for symbolic processing: 0.05479 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Optimal feedback f_k 0.466972876644368870
f(x_0) 0.000000000000000000
Solver: PENBMI. EXIT=0. INFORM=0.
BMI Solver PENBMI 2.1
Solution obtained.
FuncEv 13 GradEv 13 Iter 13 MinorIter 31
Elapsed time: 0.002000 sec.
K_opt =
-0.3634 -0.1741
