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.