Sliding Mode Control for Markov Jump Singularly Perturbed Systems Under Piecewise Homogeneous Stochastic Communication Protocol
研究了存在外部干扰和通信约束的马尔可夫跳变奇异摄动系统的滑模控制问题，首次引入分段齐次马尔可夫链调度随机通信协议，构建三层非平稳马尔可夫模型，并设计了自适应控制器和滑模面，通过仿真验证了方法的有效性。
This work involves the sliding mode control (SMC) issue for a class of Markov jump singularly perturbed systems (MJSPSs) under consideration of unmatched external disturbances and communication constraints. For the first time, the piecewise homogeneous Markov chain (MC) which depends on the system mode and the controller mode is applied to control the scheduling of stochastic communication protocol (SCP), so that the MCs in the system models, the controller and the SCP constitute a three-layer nonstationary Markov model (NMM). This model perfectly describes the different objects of the three MCs and reflects the mutual regulation among them. The critical issue is to devise an adaptive controller and a sliding surface (SS) simultaneously under SCP scheduling. By applying a standard singular sliding mode surface, an appropriate nonstationary SMC law is established to promise the accessibility of the SS and the stability of the closed-loop system (CLS), and meet the expected performance indicator. Further, using the mode-dependent Lyapunov function and piecewise homogeneous Markov model method, sufficient criteria are obtained. The specific expression of the control gain is obtained by matrix decoupling technology. Finally, a numerical simulation is furnished to testify the correctness of the conclusion.