Solution for an LMI using solver 'SDPT3'

[Najla Pary]

Hi everyone,

I have trouble with finding solution to a Linear Matrix Inequality that is related to my MTech Project.

The LMI has several unknown variables, which are in the form of matrices. I am trying to solve it using SDPT3 solver, which is mentioned in the literature related to this work.

I am attaching both my Matlab code and the corresponding reference paper with this post.

The error that is shown is 'Infeasible problem.'. But it is a feasible LMI problem as per the reference paper. So some error must have occurred in my code or in the way I have formulated the unknown matrices.

Kindly help me resolve this!!

PS:
1) I have tried with a different solver, which is FMINCON
2) I have given 'full' while declaring semidefinite variables using sdpvar command, since the matrices are not symmetric
3) The problem is an optimization problem, where it is required to minimize an objective function subject to a constraint, which is an LMI. I have tried solving only the constraint, without considering the objective function.
Even then it is found to be infeasible

Regards and waiting for a solution,

Najla Pary

[Johan Löfberg]

You talk about LMIs (and then you would never ever use fmincon!) but none of your constraints are LMIs (because the involved matrices are not symmetric)

>> Constraints

++++++++++++++++++++++++++++++++++++++++++++++++++++

|   ID|                                  Constraint|

++++++++++++++++++++++++++++++++++++++++++++++++++++

|   #1|                Element-wise inequality 44x1|

|   #2|   Element-wise inequality (quadratic) 342x1|

++++++++++++++++++++++++++++++++++++++++++++++++++++

>> P

Linear matrix variable 14x14 (full, real, 28 variables, eigenvalues between [0,0])

You've failed in setting up the matrices correctly

[Najla Pary]

Dear Johan,

I think I have understood the mistake. Now it is successfully getting solved. 

I will get back to you if I have any further doubts.

Thank you

[Najla Pary]

Dear Johan,

I have again met with problems in my code.

No i am getting error 'Lack of progress'

Also, the values of controller parameters obtained (Ac, Bc, Cc and Dc) are not as expected. They are either too small or too large.

What could be the problem??

I am attaching the new code with this post.