(Scalar/Matrix) Constraints Numbers

[Hailong Chen]

Dear Prof. Johan Löfberg,

Hope you enjoyed the holiday season!

I have a question about SOS program. The thing is that I tried to impose some contraints on the polynomial functions such that they satisfy some SOS constraints. Then I found a strange phenomenon. For the nomial system, if I want to enforce a scalar SOS constraints to enforce the negative definiteness of the derivative of Lyapunov function, the number of constraints is proper. However, when I try to address the uncertainty, i.e., to enforce the constraints in the form of SOS matrix constraints to guarantee the negative definiteness of the derivative of Lyapunov function for the system matrices located in ellipsoild, the constraints number increase stremendously.

The number of (scalar/matrix) SOS constraints is reported as follow:

Nominal systems: Constraints: 346; Scalar variables: 1; Matrix variables: 3.

Uncertainty systems: Constraints: 113131; Scalar variables: 60878 Matrix variables:3.

I admit that the SOS program for the uncertain case is more complex than the nomial one. However, the difference is quite incredible.

Nominal:

Uncertainty: (replace (10b) by the following one)

Best Regards,

Hailong

 

[Johan Löfberg]

Without a small reproducible example, it is impossible to say where you've gone wrong.