基于切换时滞系统理论的多智能体系统有限时间接力协调控制

This proposal studies the finite-time relay coordinated control of multiagent systems with time delays based on the theory of switched delay systems. In practice, due to the limitation of the agent's energy, it is difficult to ensure the continuous running of the whole multiagent system, so the expected asymptotic results cannot usually be achieved. In addition, if some of the agents are not able to participate in the coordinated control tasks during the operation of the system, the anticipant coordinated control task will fail. The emergence of these above-mentioned problems has brought difficulties and challenges for the research of multiagent systems. In this proposal, firstly based on the algebraic graph theory and impulse theory, an impulsive switched delay system will be established. For the case of agents with the same time delay, sufficient conditions for the finite-time relay coordinated control will be established using the finite-time Lyapunov stability theory. The finite-time cooperative relay coordinated control protocol will also be provided. Then, based on the obtained results, the finite-time cooperative relay coordinated control of multiagent systems with non-identical delays will further be investigated. Finally, the theoretical results will be applied to the coordinated control of wheeled robots. This proposal will reveal the effects of pulse information, time delays, and switching topologies on the convergence rate of multiagent systems. The obtained results will also provide theoretical support for engineers to design the relay coordinated control algorithms of multiagent systems with time delay constraints.

本项目基于切换时滞系统理论研究具有时滞的多智能体系统有限时间接力协调控制问题。在实际中，由于智能体自身能源的限制，难以保证系统持续运行，导致渐近收敛的结论通常难以实现。此外，如果系统运行过程中一些智能体由于某些原因不能参与协调控制任务，整个任务将会失败。上述问题的出现为多智能体的研究带来了困难和挑战。本项目首先基于代数图理论和脉冲理论，建立脉冲切换时滞系统模型。针对各个智能体具有相同时滞的情形，利用有限时间Lyapunov稳定性理论建立有限时间接力协调控制的条件，并设计接力控制器。随后基于上述成果，完成各个智能体具有不同时滞约束的有限时间接力协调控制研究。最后，将理论成果应用到轮式机器人的协调控制中。本项目将揭示脉冲信息、时滞以及切换拓扑对系统收敛速度的作用规律，为工程人员在时滞约束下设计多智能体系统的接力协调控制算法提供理论支撑。

该项目在充分考虑网络拓扑结构、外部扰动、网络攻击、系统模型等多方面因素的情况下，对多智能体协调控制问题开展了研究。提出了多智能体接力协调控制问题，给出了智能体间接力条件，建立了接力协调控制的模型，给出了接力协调控制协议设计；在智能体存在节点失效的情形下，提出了一种主动替换的策略，利用泰森多边形动态划分实现了替换角色的选择，设计的控制协议能保证闭环系统在有限时间内实现协调控制任务；通过引入多胞型拉普拉斯矩阵并且构建一个调度函数，解决了连续时变的通信拓扑图的刻画问题，基于李雅普诺夫函数法稳定性理论和滑模控制理论，为智能体设计了自适应滑模控制协议，所设计的协议能保证多智能体系统在有外部扰动的情况下实现协调控制任务；通过引入拓扑依赖攻击频率和攻击长度概念，并且将具有网络攻击的多智能体的闭环动态方程建模为切换系统，基于切换系统理论给出了多智能体系统在具有满足部分限定条件的网络攻击下的协调控制结果，设计了智能体的协调控制协议，给出了保证协调控制任务的充分性条件；把具有网络攻击的多智能体系统建模为相应的切换系统，结合李雅普诺夫稳定性理论稳定性条件和切换控制理论并对网络攻击的频率和攻击长度施加限制条件，给出了保证闭环系统稳定的控制协议，并给出了事件驱动机制设计。本项目所取得的成果丰富了多智能体协调控制研究理论，为多智能体系统的协调控制应用提供了理论依据。