Adaptive fault tolerant control for a class of nonlinear stochastic systems with double actuators

This paper studies the stabilization problem for a class of nonlinear systems with double actuators and stochastic noises. Different from the most existing results, two independent Markovian variables have been introduced to describe the statuses of the respective actuators, therefore, the actuator failure times, modes are stochastic and independent of each other. Two main difficulties arise: (1) how to establish the infinitesimal generator for systems involving double Markovian variables and stochastic noises; (2) how to cope with the extra transition rate related terms appeared in the infinitesimal generator. Firstly, by taking into account of the involving double Markovian variables and stochastic noises, the infinitesimal generator, stability criterion and so on have been redefined. Then, by employing a backstepping technique, an adaptive fault tolerant control scheme has been developed, which ensured the boundedness in probability of all the closed-loop signals. Finally, an example is presented to show the effectiveness of the proposed scheme.