Adaptive fault-tolerant control for stochastic nonlinear systems based on time-varying Markov jump model

Although significant progress has been made in the field of adaptive fault-tolerant control (FTC), the majority of existing studies concentrate on accommodating limited number of actuator failures within a deterministic framework. This paper investigates the adaptive FTC problem for stochastic uncertain nonlinear systems based on time-varying Markov jump models. A joint Markov process with independent components is employed to characterise infinite number of random jumps in control inputs as well as plant parameters. An adaptive backstepping fault-tolerant controller is proposed, which utilises a single parameter estimator to deal with both the multiplicative and additive actuator failures of unknown bounds together, without requiring access to or synchronisation with regime switching of the joint Markov process. Stability analysis shows that with appropriate design parameters, the tracking error can converge into an arbitrarily small residual set in the sense of 4th moment while closed-loop signal boundedness in probability is guaranteed. Simulation results further demonstrate that our proposed adaptive FTC method is capable of accommodating stochastic uncertainties arising from plant parameters, actuator failures and unknown covariance noises.