‘SOS.model', 2

[Hailong Chen]

Dear Prof.Johan Löfberg,

I've already read the content in https://yalmip.github.io/Strictly-feasible-sum-of-squares/. But I still don't understand the details of it.

The things are as follows.

When I use the default setting to solve an SOS program, the output log tells me that the program is feasible, but with the hint:

-> Although the solver indicates no problems,
-> the residuals in the problem are really bad.
-> My guess: the problem is probably infeasible.
-> Make sure to check how well your decomposition
-> matches your polynomial (see manual)
-> You can also try to change the option sos.model
-> or use another SDP solver.

Therefore, I set sos.model as 2. At this time, the program is feasible. Does it mean that the issue is fixed?

It often outputs the warning:

MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col '' (12) of matrix 'A'.

I already read the related conversations. But it shows me that "it very often signals bad models, and might lead to bad or sensitive solutions".

The thing is that I use the SOS program to design a controller and find a Lyapunov function. When I applied the solution to draw the ROA and the trajectories. The trajectories converge, and the system is asymptotically stable.

Can I trust the feasible solution to some extent?

Best regards,

Hailong Chen

[Johan Löfberg]

it indicates that the numerics is really bad in the model as it fails to siolve one form but (claims) to solve in another. strenghtened by the fact that the solver complains about your data too.

whether the solution is useful is up to your modelling. if V is a lyapunov function and you only required V>=0 and Vdot<=0 then you have little margin for numerical error, but if the model is V>=x^2 and Vdot<=-x^2 you have a lot of margin for error

[Hailong Chen]

I see! Thank you very much!

Best regards,

Hailong