Chapter 5 - Nonlinear time-delay system identification

Abstract

This chapter first researches parameter estimation problems for a Hammerstein input nonlinear system with state time delay. Combining the linear transformation and the property of the shift operator, the Hammerstein state-space system is equivalent to a bilinear parameter identification model. The gradient-based and least squares-based iterative parameter estimation algorithms are used for identifying the state time-delay system, and the proposed iterative algorithms make full use of all data at each iteration, which can produce highly accurate parameter estimation. Then, it presents a combined parameter and state estimation algorithm for a time-delay system described by the observer canonical state-space model based on the bias compensation. The state-space system with time delay is transformed into an input–output representation by eliminating the state variables. According to the obtained identification model, a bias compensation least squares algorithm is proposed for estimating the system parameters and states interactively by adding the bias correction term into the least squares estimates. The proposed algorithm can generate an unbiased parameter estimate.