Nonlinear System Identification Based on a Fock Space Framework.

摘要

A method is presented for the identification of a nonlinear system represented by an operator V:E yields Y, where the input space E is a separable Hilbert space over the field of complex numbers and the output space Y is the Sobolev space H(n)-squared of complex-valued functions y on an interval I of the real line such that all the k-th derivatives of y with respect to t, k=O,...,n-1, are absolutely continuous and the n-th derivative of y with respect to t is an element of L-squared (I). The above developments permit us to obtain the solution to our nonlinear system identification problem as the solution to an appropriate minimum norm problem in B(n)-squared (I.F sub rho(E)). Procedures for obtaining both the noncausal and causal solutions are given. We also introduce the concept of 'epsilon-causality', which is weaker than that of causality, and derive an epsilon-causal solution to our problem. The case when measurement errors are present is finally considered.The results are illustrated by the computer simulation of a simple example in which very good agreement with the theory is obtained over a wide time-interval.