Adaptive Fault-Tolerant Control for Time-Delay Nonlinear Systems with Stochastic Actuator Failures

In [18], a class of nonlinear systems with stochastic actuator failures have been studied. Stochastic functions related to Markovian variables have been introduced to describe the failure scaling factors for each actuators. In this paper we consider the kind of systems involving state-delay, which is much more practical, and adaptive fault-tolerant control problem has been studied. Two main challenges arise: how to establish the infinitesimal generator for systems involving multi-Markovian variables and state-delay simultaneously; then how to handle the delayed terms and the extra transition rate related ones appearing in the wisely designed Lyapunov-Krasovskii functional. By proposing an adaptive fault-tolerant control scheme, the existence and uniqueness of the solution process to the closed-loop system is guaranteed and the boundedness in probability of all the closed-loop signals can be ensured. An example is worked out to illustrate the effectiveness of the proposed scheme.