Average Predictor-Feedback Control Design for Switched Linear Systems

TL;DR

This paper introduces an average predictor-feedback control law for switched linear systems with time-dependent switching, ensuring exponential stability without restrictions on delay or dwell time, by approximating the system with an average model.

Contribution

The paper proposes a novel average predictor-feedback control method for switched systems, addressing the challenge of unknown future switching signals and providing stability guarantees.

Findings

The closed-loop system is exponentially stable under the proposed control law.

Stability depends on the closeness of plant parameters to the average system.

Numerical simulations confirm the effectiveness of the average predictor-based control.

Abstract

We develop an input delay-compensating feedback law for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be unavailable at current time, the key design challenge is how to construct a proper predictor state. We resolve this challenge constructing an average predictor-based feedback law, which may be viewed as an exact predictor-feedback law for a particular average system without switching. We establish that, under the predictor-based control law introduced, the closed-loop system is exponentially stable, provided that the plant's parameters are sufficiently close to the corresponding parameters of the average system. In particular, the allowable difference is inversely proportional to the size of delay and proportional to the dwell time of the switching signal. Since no restriction is imposed on the size of delay or dwell time themselves, such a limitation on the parameters of each mode is inherent to the problem considered (in which no a priori information on the switching signal is available), and thus, it cannot be removed. The stability proof relies on two main ingredients-a Lyapunov functional constructed via backstepping and derivation of solutions' estimates for the difference between the average and the exact predictor states. We present consistent, numerical simulation results, which illustrate the necessity of employing the average predictor-based law for achieving stabilization and desired performance of the closed-loop system.