Adaptive fault-tolerant stabilization for nonlinear systems with Markovian jumping actuator failures and stochastic noises

In this paper we consider the fault-tolerant stabilization problem for a class of nonlinear systems with uncertain parameters. Uncertainties caused by Markovian jumping actuator failures and stochastic noises are also taken into consideration. Different from most existing results, the number of actuator failures may be infinite and stochastic functions related to multi-Markovian variables have been introduced to denote the failure scaling factors for the actuators, which is practical, but challenging. Three main difficulties arise: first is how to establish fundamentals for systems involving multi-Markovian variables and stochastic noises, including the joint transition probability, the infinitesimal generator, the existence and uniqueness of the solution and so on; second is how to handle the extra transition rate related terms appearing in the infinitesimal generator of the Lyapunov function; last is how to cope with the involved higher order Hessian term in the Itô stochastic differentiation. By proposing a new adaptive fault tolerant control scheme, the boundedness in probability of all the closed-loop signals has been ensured. An example of altitude fault-tolerant control for a generic hypersonic air vehicle is presented to show the effectiveness of the proposed scheme.