Adaptive Fault-Tolerant Sliding Mode Control for Itô-Type Stochastic Time-Delay Markov Jump Systems with Partly Unknown Transition Probabilities

This study addresses the challenge of designing an adaptive sliding mode controller for a class of nonlinear Markov jump systems. These systems are characterized by unmeasurable states, partially unknown transition probabilities, and uncertainties arising from matched external disturbances and modeling inaccuracies. In control design and analysis, the nonlinear Markov system in which both the linear term and specific information about the upper bound in the external disturbance term are unknown. To enable descending equivalent sliding mode motion to regulate the dithering phenomenon in a controlled system, an integral sliding surface is established to achieve chattering suppression via descending equivalent sliding motion. A key theoretical contribution is the rigorous proof that the proposed control law ensures both finite-time reachability of the sliding surface and mean-square stability of the closed-loop trajectories. Comparative simulation results demonstrate that the proposed approach achieves a state estimation RMSE of 0.175, which is 48.0% lower than conventional sliding mode control (0.337) and 3.3% lower than observer-based sliding mode control without fault compensation (0.181). The controller reduces control chattering by 75.2% compared to conventional SMC (total variation from 64.4 to 16.0), achieves sliding surface reachability within 0.42s, and maintains effective fault estimation with an average RMSE of 0.138 for time-varying actuator efficiency factors. These quantitative improvements validate the effectiveness of the proposed fault-tolerant mechanism.