Ren Lu, Li Man, Liu Jian, Sun Changyin
School of Artificial Intelligence, Anhui University, Anhui 230601, China.
Department of Automation, University of Science and Technology of China, Hefei 230027, China.
ISA Trans. 2022 Feb;121:130-139. doi: 10.1016/j.isatra.2021.03.031. Epub 2021 Apr 19.
In this paper, the cluster synchronization problem for heterogeneous nonlinear systems with input saturation is studied under both fixed and switching topologies. The distributed feedback controllers are first designed by low gain technique to deal with the input saturation. Sufficient conditions for reaching semi-global cluster synchronization are derived by utilizing the algebraic graph theory, Lyapunov method, and low gain technique. It is shown that the semi-global cluster synchronization problem can be solved by using the proposed synchronization protocols on some preconditions for both fixed and switching topologies. Moreover, under the switching topology, the lower bound of the total activation time for the derived topology with a directed spanning tree is explicitly specified. Finally, some examples are presented to demonstrate the effectiveness of the proposed theories.
本文研究了具有输入饱和的异构非线性系统在固定拓扑和切换拓扑下的簇同步问题。首先通过低增益技术设计分布式反馈控制器来处理输入饱和。利用代数图论、李雅普诺夫方法和低增益技术，推导了实现半全局簇同步的充分条件。结果表明，在固定拓扑和切换拓扑的一些前提条件下，使用所提出的同步协议可以解决半全局簇同步问题。此外，在切换拓扑下，明确给出了具有有向生成树的派生拓扑的总激活时间的下界。最后，给出了一些例子来证明所提理论的有效性。
