Block pulse function approach for the identification of Hammerstein model non-linear systems

Abstract

Two recursive algorithms based on block pulse functions are presented for identifying continuous Hammerstein models of non-linear systems with (i) a state space model and (ii) an input–output model. Since the continuous non-linear systems are transformed approximately into the corresponding difference equations via block pulse functions, these recursive estimation algorithms can easily be obtained using a derivation similar to that of the discrete-time models expressed by difference equations. Both algorithms derived here are simple and straightforward, and can easily be implemented on-line. As discussed in this paper, these algorithms can also be extended to the identification of certain continuous non-linear systems with a feedback loop or with time delays. The illustrative examples show that these recursive algorithms give satisfactory results for the identification problems of certain continuous non-linear systems.