In this paper, a novel asynchronous sliding mode-based learning control is proposed for a class of discrete-time semi-Markov jump systems, in which the probability density function of sojourn-time is dependent on two consecutive modes. The asynchronous switching characteristic is employed for the nonsynchronization between the controller and the jump modes. Based on the discrete-time semi-Markov kernel and multiple-Lyapunov functions, sufficient conditions are provided to guarantee the $\sigma$-error mean-square stability of the sliding mode dynamics. Furthermore, a recursive sliding mode learning controller is designed such that the sliding modes can be driven onto the designed sliding surface and the chattering caused by the asynchronous switching and mode jump can be effectively suppressed. Finally, numerical simulations on the continuous stirred tank reactor system are given to demonstrate the effectiveness and potential of the proposed techniques.

本文针对一类离散时间半马尔可夫跳跃系统提出了一种新颖的基于异步滑模的学习控制，其中逗留时间的概率密度函数依赖于两个连续模式。异步切换特性用于控制器和跳跃模式之间的不同步。基于离散时间半马尔可夫核和多李雅普诺夫函数，提供了充分条件来保证$\sigma$-滑模动力学的误差均方稳定性。此外，设计了一个递归滑模学习控制器，使得滑模可以被驱动到设计的滑模面上，并且可以有效地抑制异步切换和模式跳跃引起的颤振。最后，对连续搅拌釜反应器系统进行了数值模拟，以证明所提出技术的有效性和潜力。