Instrumental-variable methods for identification of Hammerstein systems

Abstract Consistency conditions for instrumental-variable methods applied to Hammerstein models are derived and analysed. It is necessary to have a model that is not over-parametrized and an input that is ‘ strongly persistently exciting ’, i.e. the inputs and their powers are jointly persistently exciting. Some specific choices of the instruments are proved to give consistency. Those instruments are formed as filtered inputs and powers of the input. Consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive-real. The vector of instruments is, in general, of larger dimension than the parameter vector. It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate. Some simulations using the IV variants proposed in this paper are also included.