转移概率部分未知下Markov跳变系统的滑模控制  

Sliding mode control of Markov jump system with partially unknown transition probabilities

作　　者：李媛[1] 谭旭峰 董知非 于忠鑫 LI Yuan;TAN Xu-feng;DONG Zhi-fei;YU Zhong-xin(School of Science,Shenyang University of Technology,Shenyang 110870,China;SPIC Northeast New Energy Development Co.Ltd.,Shenyang 110000,China)

机构地区：[1]沈阳工业大学理学院,沈阳110870 [2]国家电投东北新能源发展有限公司,沈阳110000

出　　处：《沈阳工业大学学报》2023年第2期214-220,共7页Journal of Shenyang University of Technology

基　　金：国家自然科学基金项目(62103289)。

摘　　要：针对系统中含有两个相互独立的Markov链,且转移概率不完全已知的时滞不确定离散Markov跳变系统的滑模控制(SMC)问题,通过考虑参数不确定性的匹配条件,设计离散积分型滑模面.利用时滞分割技术构造含加权参数的Lyapunov-Krasovskii函数,得到系统随机稳定的充分条件,根据指数趋近律的到达条件设计滑模控制律,使得系统的状态轨迹能够到达所设计的滑模面.数值仿真结果表明,该方法具有一定的有效性.Aiming at the sliding mode control(SMC) problem for uncertain discrete-time Markovian jump systems(MJSs) with two time-delay Markov chains under incompletely known transition probabilities, the discrete integral sliding surface was designed by considering the matching conditions for parameter uncertainty. Lyapunov-Krasovskii function with weighted parameters was constructed by using the delay-fractioning approach, and the sufficient conditions for stochastic stability of the system were obtained. The sliding mode control law was designed according to the reaching condition of exponential reaching law, so that the state trajectory of the system can reach the designed sliding surface. Numerical simulation results show that the as-designed method is effective.

关 键 词：MARKOV跳变系统 随机稳定 时变时滞 转移概率 时滞分割法 滑模控制 LYAPUNOV-KRASOVSKII函数 积分型滑模面 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]