Output-feedback stochastic nonlinear adaptive control against Markovian jump actuator failures

Designing an output-feedback controller for stochastic uncertain nonlinear systems with Markovian jump actuator failures presents significant technical challenges, primarily because of i) the presence of mismatched parametric uncertainties and non-vanishing stochastic disturbances, which introduce substantial nonlinearities into system dynamics; ii) the unavailability of the overall control input due to actuator failures governed by a joint Markovian process, which obstructs the construction of adaptive observers; and iii) the emergence of an 'interconnected' term in Lyapunov analysis caused by Markovian jump failures of multiple actuators, whose impacts on system stability cannot be mitigated by simply summing up a series of Lyapunov functions. This article investigates the stochastic nonlinear adaptive control problem under Markovian jump actuator failures via output-feedback. To clearly illustrate our method, we begin with single-loop systems. By lumping uncertain plant and failure parameters together, the controlled system is re-expressed as an output-feedback canonical form, then a kind of high-gain K-filter is applied to reconstruct unmeasured states. By employing the stochastic Lyapunov design approach and the backstepping technique, an adaptive fault-tolerant controller is proposed to address Markovian jump actuator failures. Next, the results are extended to large-scale systems, in which a novel decentralized control strategy is developed to cope with uncertain interactions. Besides ensuring all the closed-loop signals are globally ultimately bounded in probability, it is also shown that the tracking error can be limited to an arbitrarily small residual set in the mean quartic sense. Simulation studies are conducted to confirm our theoretical findings.