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

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.