Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems

This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods,respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.