I am working on system identification problem. The question of convexity come up, and I am wondering if transfer function model and state space model suffer from the local minimum issue?
If you have a black box model and it's linear, why not go with a subspace identification algorithm? You won't have to deal with convexity issues. However, if you want to find an optimal system, then you will likely have convexity issues.
I am not sure, if I understood the question. Convexity and local minimum are related to optimization problems and functions which are minimized. Models like transfer functions or state space representations are not related to these issues. If the problem consists in the fact that you are using a numerical optimization algorithm as a method for parameter estimation and you are minimizing a function which have local minimum, then yes this could be a problem but from the optimization algorithm and not from model itself. You can change the identification methods as suggested Jose or you can change the cost function.
I'm doing closed loop identification using MATLAB tool box with ssest and interior-point algrithm. I was lucky to arrived at some parameter sets that are preferable when I verified it with open loop response, but if I initialized the parameter set with randon values I hardly would arrived at the preferable parameter sets.
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