Re: H infinity Observer using Yalmip with different solvers( problem of minimization)

[Johan Löfberg]

When I minimize gamma, the solution is strictly feasible, so I don't see your claim

>> check(F)

 

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

|    ID|               Constraint|   Primal residual|   Dual residual|

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

|    #1|        Matrix inequality|            0.2564|       1.401e-11|

|    #2|        Matrix inequality|            0.2029|       1.401e-11|

|    #3|        Matrix inequality|           0.22761|      1.4038e-12|

|    #4|        Matrix inequality|        3.9727e-08|      1.4056e-12|

|    #5|        Matrix inequality|           0.19191|      1.4005e-11|

|    #6|        Matrix inequality|           0.26916|      1.4005e-11|

|    #7|        Matrix inequality|           0.20297|      1.4005e-11|

|    #8|        Matrix inequality|           0.27923|      1.4006e-11|

|    #9|        Matrix inequality|        2.2779e-08|       1.082e-07|

|   #10|        Matrix inequality|           0.17922|      3.3573e-08|

|   #11|        Matrix inequality|          0.088652|      4.9213e-09|

|   #12|        Matrix inequality|           0.11399|      5.2436e-09|

|   #13|   Elementwise inequality|         5523.1039|      1.4011e-11|

|   #14|   Elementwise inequality|        55116.0233|      1.4038e-12|

|   #15|   Elementwise inequality|         5525.0229|      1.4007e-11|

|   #16|   Elementwise inequality|         5524.7823|      1.4007e-11|

|   #17|   Elementwise inequality|           0.14684|      5.2241e-07|

|   #18|   Elementwise inequality|        7.2473e-08|          1.0583|

|   #19|   Elementwise inequality|           0.38838|      1.9736e-07|

|   #20|   Elementwise inequality|           0.39238|      1.9532e-07|

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

However, some of the solutions are horrible (look at K21 for instance!), which is a common phenomena in Hinf control, the optimal controller is a bad controller as it pushes some poles to infinity etc, making them useless in practice as they become extremely sensitive to numerical implementation etc. That's what you are experiencing

[Issam CHEKAKTA]

Thank you professor for the reply, so are you saying that the minimization is done properly and my Lmis are well written!. I get problem 4 ( numerical problems) using sedumi.

[Johan Löfberg]

The Hinf problem is ill-posed, so no surprise that some solvers will suffer from numerical problems as the optimal solution  cannot be attained (some of the K variables tend to infnity). Estimate what the optimal gamma is, and then solve a feasibility problem where you target a gamma, say, 5% larger, or add a penalty on involved variables etc

[Issam CHEKAKTA]

thanks professor, I'm gonna tweak some parameters to find the optimal gamma manually and see if that gives me some good results, 

[Johan Löfberg]

the value 1.058 from sedumi looks reasonably trustworthy

[Issam CHEKAKTA]

okay, i will start from this value and see the response, thank you for you time professor, i appreciate it a lot