Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively.

许多实际系统不仅涉及参数更改，还涉及环境条件的突然变化，这通常会导致不可预测的拓扑切换。本文研究了具有半马尔可夫切换拓扑的单侧Lipschitz非线性多智能体系统（MAS）的脉冲一致问题。与现有的马尔可夫链建模方法不同，采用半马尔可夫链合理地描述了这种随机发生的变化。为了应对多主体系统中的通信和控制成本约束，采用了分布式脉冲控制方法来解决领导者与跟随者的共识问题。除此之外，为了获得更广泛的非线性应用范围，单边条件被微妙地发展到控制器设计中，并且结果与使用Lipschitz条件的传统方法所获得的结果不同（请注意，现有结果通常仅适用于Lipschitz常数较小的情况）。基于累积分布函数的特点，类Lyapunov函数理论和脉冲微分方程，利用所提出的脉冲控制协议保持了多智能体系统的渐近均方共识。最后，提出了一种解释性仿真来最终验证所提出方法的正确性。根据类Lyapunov函数和脉冲微分方程的理论，通过提出的脉冲控制协议保持了多智能体系统的渐近均方共识。最后，提出了一种解释性仿真来最终验证所提出方法的正确性。根据类Lyapunov函数和脉冲微分方程的理论，通过提出的脉冲控制协议保持了多智能体系统的渐近均方共识。最后，提出了一种解释性仿真来最终验证所提出方法的正确性。