Parameter Estimation of Switched Hammerstein Systems

TL;DR

This paper proposes a recursive least squares method for estimating parameters of switched Hammerstein systems with arbitrary switching laws, ensuring strong consistency in different excitation scenarios.

Contribution

It introduces the concept of 'intrinsic switch' to handle data coupling and proves the strong consistency of parameter estimates under various input conditions.

Findings

Strong consistency of RLS estimates is established.

The method effectively handles arbitrary switching laws.

Simulation verifies theoretical results.

Abstract

This paper deals with the parameter estimation problem of the Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis.