Recursive identification of hammerstein systems with hard input nonlinearities

Hard nonlinearities are often encountered in practice, which may severely limit the performance of industrial systems. This work focuses on recursive parameter estimation problems of Hammerstein systems with hard input nonlinearities. To date, few of the previous contributions assume the input nonlinear block is noninvertible and discontinuous, which is the main contribution of this report. It is also noted the direct motivation of this work is to derive recursive estimators for some on-line control strategies (e.g. adaptive control algorithms). With parameterization of the input nonlinear block based on a piecewise-linear function, the recursive identification method is derived from a recursive least-squares algorithm. Theoretical analysis indicates that the convergence of parameter estimation can be guaranteed in the presence of persistent excitation. Simulation results show the wide applications of the recursive parameter estimation scheme in identifying Hammerstein models with hard input nonlinearities, even in the case of noninvertible discontinuous input nonlinearities.