Fault‐tolerant control for Markovian jump systems with general uncertain transition rates against simultaneous actuator and sensor faults

Abstract

SummaryThis paper investigates the problems of simultaneous estimations of actuator faults and sensor faults, as well as fault‐tolerant control schemes for a class of Markovian jump systems with general uncertain transition rates. In a general uncertain transition rate matrix model, transition rate may be completely unknown, or one can only acquire its estimated value, which makes the design much more challenging. First, the original system is transformed into a descriptor one by extending the sensor faults to be parts of state vector. Then, a robust stochastic adaptive observer is designed for the descriptor system with the actuator fault being adjusted by an adaptive law. On the basis of the estimated states as well as estimated actuator and sensor faults, a fault‐tolerant control strategy is proposed to make the resulting closed‐loop system stable in the presence of the actuator fault. Sufficient existence conditions of the observer and controller are derived in terms of linear matrix inequalities. Finally, three practical examples are given to validate the high efficiency of our proposed method. Copyright © 2017 John Wiley & Sons, Ltd.