IEEE Trans Cybern. 2017 Apr;47(4):898-907. doi: 10.1109/TCYB.2016.2532898. Epub 2016 Mar 8.
This paper is concerned with the problem of average consensus control for multi-agent systems with linear and Lipschitz nonlinear dynamics under a switching topology. First, a proportional and derivative-like consensus algorithm for linear cases with a time delay is designed to address such a problem. By a system transformation, such a problem is converted to the stability problem of a switched delay system. The stability analysis is performed based on a proposed Lyapunov-Krasoversusii functional including a triple-integral term and sufficient conditions are obtained to guarantee the average consensus for multi-agent systems under arbitrary switching. Second, extensions to the Lipschitz nonlinear cases are further presented. Finally, numerical examples are given to illustrate the effectiveness of the results.
本文研究了具有线性和 Lipschitz 非线性动力学的多智能体系统在切换拓扑下的平均一致性控制问题。首先，针对具有时滞的线性情况设计了一种比例导数型一致性算法，以解决这一问题。通过系统变换，将该问题转化为切换时滞系统的稳定性问题。基于包含三重积分项的李雅普诺夫-克拉索夫斯基泛函进行稳定性分析，并给出了在任意切换下保证多智能体系统平均一致性的充分条件。其次，进一步将其推广到 Lipschitz 非线性情况。最后，通过数值例子验证了所得结果的有效性。
