Hammerstein model identification: the case of piecewise-polynomial static-gain

We are considering the problem of identifying Hammerstein models, including a nonlinear static gain in series with linear dynamics. We particularly focus on static gains that are piecewise polynomial within a finite interval. For this class of models we develop an identification scheme with the following main features: (i) a dynamics-oriented parameterization and a static-gain-oriented parameterization, (ii) a parameter estimation algorithm associated with each parameterization, (iii) a persistently exciting input signal. The parameter estimates thus obtained are shown to converge to their true values, yielding asymptotically the true model.