Sliding mode learning control of discrete-time singular semi-Markov jump systems under unknown actuator faults

This paper investigates the sliding mode learning control problem for discrete-time singular semi-Markov jump systems with unknown actuator faults. Traditional sliding mode learning control is no longer applicable to singular systems due to the presence of singular matrices, and existing methods neglect relativity among system parameters and modes. A sliding mode learning control strategy suitable to discrete-time singular semi-Markov jump systems is proposed. First, a fault observer is designed to achieve online prediction and real time compensation for unknown actuator faults, effectively mitigating the impact of faults and mode jumps on system performance. Second, by constructing a mode independent common sliding surface and combining the semi-Markov kernel with singular value decomposition techniques, a sufficient criterion for the σ-error mean-square admissibility of sliding mode dynamics is deduced. Moreover, conditions required for the parameters in sliding mode learning control are provided to ensure the reachability of the sliding surface. Finally, the effectiveness of the proposed method is verified through simulation of a single-link robotic arm model.