Hammerstein System Identification in Presence of Hard Memory Nonlinearities

Abstract

Most works on Hammerstein system identification have focused on the case of memoryless nonlinearities characterised by a static relation u = F(v,θ) where θ is a vector of unknown parameters (Figure 21.1). For a long time, the function F(v,θ) has been assumed to be of known structure (e.g. polynomial), continuous in v and linear in θ (see e.g. Chapters 3 and 5 and reference list therein). Hard nonlinearities of known type have been considered in [1, 4, 6, 8]. Then, F(v,θ) may be nonlinear in θ and discontinuous in v. The case of memoryless nonlinearities F(v) with no prior knowledge has been dealt with in [5]. Hammerstein system identification in presence of memory hard nonlinearities is a more challenging problem.