Robust fault-tolerant stabilisation of uncertain high-order fully actuated systems with actuator faults

This paper presents a novel fault tolerance strategy for a class of uncertain high-order fully actuated systems (FASs) with actuator faults. Recently, the FAS approaches have been rapidly developed in different fields. As a control-oriented approach, a great advantage of FAS approaches is the convenient design of controllers for the deterministic nonlinear systems which meet the full-actuation condition. However, the presence of uncertainties and faults brings more challenges. To cope with the fault tolerance issue in FAS framework, a class of uncertain FASs with multiplicative actuator faults is introduced. Based on the Lyapunov stability theory, a fault-tolerant controller is presented to robustly stabilise the considered system. Moreover, for the systems that do not meet the full-actuation condition, previous research has indicated that they may be decomposed into a fully actuated subsystem and an extra autonomous subsystem. Leveraging the theory of input-to-state stability, the proposed fault-tolerant controller is further extended to cope with the stabilisation for such compound systems with nonlinear uncertainties and actuator faults. Both provided controllers can ensure the globally uniformly asymptotically stability of the considered systems and only rely on a few general assumptions. A numerical experiment illustrates the effectiveness of the proposed method.