Identification for wiener system with discontinuous piece-wise linear function via sparse optimization

This paper presents a new approach to the identification of Wiener system consisted of an ARX subsystem followed by a static discontinuous piece-wise linear subsystem. We show this problem can be transformed into an ℓ₀-norm optimization problem, which is intractable(NP hard). To overcome this difficulty, we consider ℓ₁-norm convex relaxation inspired by compressed sensing. In the noise-free case, sufficient conditions are provided for recovering unknown parameters via ℓ₀-norm and ℓ₁-norm minimization programs. Numerical experiments demonstrate our novel algorithms perform well in noisy measurements case.