Fault Estimation and Accommodation of Fractional-Order Nonlinear, Switched, and Interconnected Systems

This discusses the fault estimation (FE) and fault accommodation (FA) methods for fractional-order systems. First, two Lyapunov theorems of input-to-state practical stability are presented for fractional-order systems, based on which an adaptive FE/FA scheme is provided. Such a scheme ensures the faulty system is input-to-state practically stable (ISpS) with respect to estimation errors. Furthermore, new results are extended to fractional-order switched and interconnected systems: for the former, an FE/FA method is proposed which fully reveals the tradeoff between the value of the fractional order, each mode’s dynamics, and switching law; for the latter, a cyclic-small-gain theorem of the fractional-order system is given under which both decentralized and distributed FE/FA methods are proposed.

I. Introduction

Faults in the automated process may result in unexpected performance and even bring disastrous results. Both fault estimation (FE) and fault accommodation (FA) are essential in complex nonlinear control systems, where FE focuses on estimating the fault information, while FA aims at adjusting the control law to guarantee the goal of a system can still be achieved despite faults. Up to now, numerous results have been given about FE and FA for various dynamic systems [1]–[4].