Adaptive preview control for piecewise discrete-time systems using multiple models

• Published in: Applied mathematical modelling Vol. 40; no. 23-24; pp. 9932 - 9946
• Main Authors: Wang, Di, Liao, Fucheng, Tomizuka, Masayoshi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2016
• Subjects: Adaptive preview control; Augmented error system; Discrete-time systems; Exponential asymptotic stability; Switching control; Adaptive preview control; Discrete-time systems; Exponential asymptotic stability; Augmented error system; Switching control
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2016.06.046

•Combining the direct multiple model adaptive control with preview control theory.•Augmented error systems with preview information are constructed.•A finite set of augmented systems covering unknown parameters is obtained.•Switching law is designed, and multi-model adaptive preview controller is derived.•Exponential asymptotic stability of closed-loop systems is discussed. In this paper, the problem of multi-model adaptive preview control is proposed for discrete-time systems with unknown piecewise constant coefficients. Following preview control theory, corresponding augmented error systems for piecewise discrete-time systems are constructed. By making use of the Heine–Borel covering theorem, a finite set of fixed augmented systems covering the range of the unknown parameters is established, and associated fixed preview controllers are derived. Based on the core idea of multi-model adaptive control, switching law of the controllers is designed, and eventually, an adaptive preview controller is obtained. The exponential asymptotic stability of closed-loop systems with large uncertainties is discussed in detail. Finally, simulation results are given to demonstrate the effectiveness of the theoretical results.