不连续耦合多智能体时滞网络化系统的协调控制

During the last few decades, the rapid development of control in networked systems has promoted widespread research and its applications in related fields. To overcome the conservatism in the existing protocols (algorithms) in the cooperative control for networked multi-agent systems, this project studies the issues of cooperative control in the delayed networked multi-agent systems with discontinuous interaction by combining the nonsmooth dynamic system theory, the modem control theory, and the delay dynamic system theory. The main research topics are as follows: Firstly, this study constructs models which can more accurately depict the networked multi-agent systems in the real world. Secondly, we provide convergence analysis for such first and second order models with and without a leader over fixed directed network topologies, respectively; we establish the conditions in which the agents achieve cooperativeness under discontinuous network connectivity, and then extend network topologies to the stochastic switching communication graphs. Finally, we analyze the robustness of coordinated behavior and cooperative control in the presence of the disturbance of time delays, system parameters and network structures. Based on the above results, we explore the mechanism of mathematical physics among the agents in the networked systems under discontinuous interaction. Furthermore, it is believed that the results of this project could lay a foundation for future theoretical research, experimental verification and practical application of the cooperative control in the networked systems.

在过去的十几年里，网络化系统的控制取得了飞速的发展，并推动了与之相关领域的研究与应用。本项目针对现有多智能体网络化系统协调控制协议(算法)的保守性，将非光滑动力系统理论、现代控制理论及时滞动力系统理论三种科学理论有机的结合起来，研究不连续耦合多智能体时滞网络化系统的协调控制问题。其目标是：构建能更精确地刻画现实世界中多智能体网络化系统模型；采用矩阵论、代数图论、Lyapunov-Krasovskii函数、频率分析法、鲁棒控制以及一些不连续控制方法给出适合上述模型的分析和设计方法；分别得到一阶、二阶(含引导者和无引导者)网络系统达到协调的条件，并将网络拓扑推广到随机切换的情形，进一步讨论在时滞、系统参数和网络结构扰动下合作行为与协调控制的鲁棒性。通过上述研究，探索这种网络系统智能体间不连续连接的数学物理机制；最终，达到为网络化系统的协调控制进一步的理论研究、实验验证和实际应用奠定基础。

本项目系统地研究了不连续耦合多智能体时滞网络化系统的协调控制问题，取得了一系列理论研究成果，完成了项目预期的研究任务。由于不连续（瞬时）耦合是网络耦合的一种重要表现形式，本项目针对一阶多智能体和二阶（包括调和振子）多智能体网络系统，在有向网络拓扑结构、输入时滞、通讯时滞、网络拓扑随机切换和控制缺失环境下对不连续耦合开展了深入的研究，主要成果是：1）针对一阶有向时滞智能体网络系统，提出了分布式瞬时耦合一致性协议，并在网络拓扑随机切换环境下，给出了网络中的智能体达到一致的判据；2）研究了具有通讯时滞和输入时滞的瞬时耦合有向调和振子系统的同步问题，结果表明，通讯时滞对耦合调和振子系统的影响大于输入时滞对其影响；3）探讨了在控制缺失环境下具有通讯时滞和输入时滞的有向调和振子系统的采样控制问题，并分析地得到了通讯时滞和输入时滞对网络系统的同步性能具有正影响；4）针对耦合简谐振子系统，提出了具有控制缺失和通讯时滞的分布式采样协议；5）研究了一类具有参考速度和输入时滞的有向二阶多智能体的同步问题，每个智能体只在某些离散时刻跟踪一个参考速度，结果显示，若系统的连通图只有一棵生成树，输入时滞小于交换信息时间间隔，且二者均小于一个给定的阀值，则系统达到渐进同步；6）针对一类二阶多智能体系统，提出了一个分布式脉冲协议，结果表明，系统的一致性状态决定于采样周期和速度阻尼增益。本项目成果为网络化系统的协调控制进一步的理论研究、实验验证和实际应用奠定了基础。