Abstract This work studies the asynchronous fault-tolerant sliding mode control for uncertain stochastic jumping systems subject to singular perturbations, in which the controller is assumed to be able to estimate the hidden system mode through a detector with a conditional probability via the hidden-Markov model. Additionally, in consideration of avoiding the system performance decreases generated by the actuator degradation, the synthesized fault-tolerant sliding mode control scheme is first employed. Through applying a common singularly perturbed parameter based sliding surface, this paper attempts to construct a proper asynchronous sliding mode control law that can ensure not only the reachability but also the closed-loop system is stable with an expected H∞ performance index. By virtue of the mode-dependent Lyapunov function and the hidden-Markov model approach, sufficient conditions are acquired. Besides, solving linear matrix inequalities for obtaining the control gain matrices are given through the convex optimization theory. Eventually, the effectiveness and feasibility of the proposed asynchronous fault-tolerant sliding mode control scheme are verified by a numerical example.

中文翻译：

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随机跳跃奇异摄动系统的异步容错控制：一种H∞滑模控制方案

摘要 本工作研究了受奇异扰动影响的不确定随机跳跃系统的异步容错滑模控制，其中假设控制器能够通过隐马尔可夫模型以条件概率的检测器估计隐系统模式。 . 此外，考虑到避免执行器退化导致系统性能下降，首先采用综合容错滑模控制方案。本文通过应用基于普通奇异扰动参数的滑动面，尝试构建适当的异步滑模控制律，该控制律不仅可以确保可达性，而且可以确保闭环系统稳定并具有预期的 H∞ 性能指标。凭借依赖于模态的Lyapunov函数和隐马尔可夫模型方法，获得了充分条件。此外，通过凸优化理论给出了求解线性矩阵不等式以获得控制增益矩阵。最后，通过数值算例验证了所提出的异步容错滑模控制方案的有效性和可行性。