Wang Tao, Wang Xuehai, Xiang Weiming
School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610000, China.
School of Computer and Cyber Sciences, Agusuta University, GA 30912, USA.
ISA Trans. 2020 Aug;103:75-85. doi: 10.1016/j.isatra.2020.03.020. Epub 2020 Mar 17.
The reachable set estimation and stabilization problems of large-scale switched systems have been investigated in this paper. To start with, a class of specific Lyapunov functions for the reachable set estimation of large-scale switched systems is proposed. Secondly, by the method of the proposed specific Lyapunov functions of the large-scale switched systems, the boundary of system state response is calculated under arbitrary switching, which might be used for the safety verification. Then, the concept of decentralized control is introduced and the decentralized state feedback controllers are developed to ensure the state trajectories of the closed-loop large-scale switched systems are limited within the estimated set and guarantee the system globally uniformly asymptotically stable. Finally, several numerical and practical examples are established to confirm the effectiveness and correctness of our results.
本文研究了大规模切换系统的可达集估计和镇定问题。首先，针对大规模切换系统的可达集估计，提出了一类特定的李雅普诺夫函数。其次，利用所提出的大规模切换系统的特定李雅普诺夫函数方法，计算了任意切换下系统状态响应的边界，该边界可用于安全验证。然后，引入分散控制的概念，并设计了分散状态反馈控制器，以确保闭环大规模切换系统的状态轨迹限制在估计集内，并保证系统全局一致渐近稳定。最后，给出了几个数值和实际例子，以验证我们结果的有效性和正确性。
