Robust Approximate Simulation for Hierarchical Control of Piecewise Affine Systems under Bounded Disturbances

TL;DR

This paper introduces a robust control method for piecewise affine systems that ensures output tracking under bounded disturbances by using a lower-dimensional linear abstraction and Lyapunov-like functions.

Contribution

It proposes a novel robust approximate simulation approach for PWA systems, improving scalability and disturbance robustness compared to existing methods.

Findings

Effective output tracking demonstrated in simulations

Method handles bounded external disturbances

Applicable to systems with multiple modes and dimensions

Abstract

Piecewise affine (PWA) systems are widely applied in many practical cases such as the control of nonlinear systems and hybrid dynamics. However, most of the existing PWA control methods have poor scalability with respect to the number of modes and system dimensions and may not be robust to the disturbances in performance. In this paper, we present a robust approximate simulation based control method for PWA systems under bounded external disturbances. First, a lower-dimensional linear system (abstraction) and an associated interface are designed to enable the output of the PWA system (concrete system) to track the output of the abstraction. Then, a Lyapunov-like simulation function is designed to show the boundedness of the output errors between the two systems. Furthermore, the results obtained for linear abstraction are extended to the case that a simpler PWA system is the abstraction. To illustrate the effectiveness of the proposed approach, simulation results are provided for two design examples.