Passivity-based adaptive fault-tolerant control for continuous-time Markov jump PWA systems with actuator faults

In this article, the issue of passivity-based adaptive fault-tolerant piecewise linear (FT-PWL) control is investigated for a class of continuous-time Markov jump nonlinear systems with actuator faults. The nonlinear space is divided into a series of subspaces and approximated by piecewise-affine (PWA) regions, such that the corresponding systems are transformed into a class of continuous-time Markov jump PWA systems. First, the switching paths between different PWA subsystems or different PWA regions within certain subsystem are optimized via a new optimal region switching paths (ORSPs) algorithm. This algorithm optimizes the loop way of searching the switching path and also reduces the number of redundant loops. Second, based on the proposed ORSPs algorithm, a novel adaptive FT-PWL controller is designed to ensure the stochastic stability and passivity of the corresponding closed-loop system. The unknown variations of actuator fault parameters are compensated via an adaptive FT mechanism. Finally, one numerical example is illustrated to show the validity and effectiveness of both developed ORSPs algorithm and proposed adaptive FT-PWL control mechanism.