马尔可夫切换拓扑下时滞多智能体系统间歇事件触发领导跟随一致性研究

Research on Leader Following Consensus Triggered by Intermittent Events in Time-Delay Multi-Agent Systems under Markov Switching Topology

摘要: 本文研究一类在马尔可夫切换拓扑和间歇通信约束下的时滞多智能体系统的领导跟随一致性问题. 智能体间的通信拓扑建模为马尔可夫切换拓扑, 基于采样控制设计一种基于邻居相对状态信息的非 周期间歇分布式事件触发一致性协议, 有效地排除 Zeno 行为. 智能体只在满足特定触发条件时进 行控制更新和信息传输, 有效地降低通信负担和能量消耗, 同时, 通过动态比例系数法, 充分考虑时 滞因素, 设置最小控制时间和最小休眠时间约束合理的选取控制宽度, 避免控制器频繁切换导致的 系统振荡和设备磨损问题. 然后, 利用李雅普诺夫稳定性理论、Kronecker 技术以及图论等方法, 推导出保证多智能体系统实现领导跟随一致性的充分条件. 最后, 通过数值仿真验证所提控制协议 的有效性和理论结果的正确性.

Abstract: This paper investigates the leader-follower consensus problem for a class of delayed multi-agent systems subject to Markovian switching topologies and intermittent com- munication constraints. The communication topology among the agents is modeled as a Markovian switching topology. Based on sampled control, a non-periodic inter- mittent distributed event-triggered consensus protocol is designed using neighboring relative state information, effectively excluding Zeno behavior. Agents perform con- trol updates and information transmissions only when specific triggering conditions are met, effectively reducing communication burden and energy consumption. Concur- rently, employing a dynamic proportional coefficient method, time-delay factors are fully considered. By setting constraints on minimum control time and minimum sleep- ing time, the control width is reasonably selected, thus avoiding system oscillations and equipment wear caused by frequent controller switching. Subsequently, using methods such as Lyapunov stability theory, Kronecker techniques, and graph theo- ry, sufficient conditions are derived to guarantee the achievement of leader-follower consensus in the multi-agent system. Finally, numerical simulations are performed to validate the effectiveness of the proposed control protocol and the correctness of the theoretical results.