复杂网络化动态系统的分析与控制

Over recent years, the analysis and control of complex networked dynamical systems has attracting increasing attention. It has become an interdisciplinary research hot-focus. Theories on networked dynamical systems have proven effective in resolving issues emerged in engineering areas, especially the ones around the cooperation of multiple robots, sensor networks, intelligent transportation systems. By virtue of the mathematical tools including algebraic graph theory, matrix theory, stability theory, theory of differential inclusion, spectrum analysis, stochastic analysis, and game theory, this project aims to deal with several representative classes of issues concerning the coordination and control in networked dynamical systems. (1) Taking into account the limitations in information communication in real systems, we consider the multi-agent systems in which information communicating is dependent on the agents' states, and analyze in detail the coordination performance of these agents. (2) We consider the multi-agent systems integrating the complex dynamics and the topological structure, and address the issues of controllability, structure controllability, and stabilizability. Furthermore we attempt to establish the conditions based on which the controllability, structure controllability, and stabilizability of the systems can be evaluated, and to derive the relationship between the controllability and stabilizability. (3) By introducing the game theory and its analysis methods into the analysis and control of the multi-agent systems, we study the assignment allocations and coordination control in the systems. The research productions of this project are expected to enrich and advance the theories on the control of complex networks.

复杂网络化动态系统的分析与控制近几年受到了众多领域研究人员的关注，已成为一个跨学科的研究热点。复杂网络化动态系统的相关理论已经被成功应用于多机器人协作、传感器网络、智能交通系统中等工程领域。应用代数图论、矩阵理论、稳定性理论、微分包含、谱分析、随机分析和博弈论等数学工具，本项目研究几类复杂网络化动态系统的协调行为和控制问题。（1）基于现实通信条件的限制，考虑通信与状态相关的多智能体系统，深入分析其协调行为；（2）考虑具有复杂动力学特征和拓扑结构的多智能体系统，研究其能控性、结构能控性和可镇定性问题，得到系统能控、结构能控和可镇定的判别条件，并建立能控和可镇定之间的关系；（3）将演化博弈理论引入多智能体系统的分析与控制中，研究多智能系统的任务分配与协调控制等问题。本项目的研究成果将进一步丰富和发展复杂系统控制相关的理论。

复杂网络化动态系统的分析与控制近几年受到了众多领域研究人员的关注，已成为一个跨学科的研究热点。复杂网络化动态系统的相关理论已经被成功应用于多机器人协作、传感器网络、智能交通系统等工程领域。本项目应用代数图论、矩阵理论、稳定性理论、微分包含、谱分析、随机分析和博弈论等数学工具，研究了复杂网络化动态系统的协调行为和控制问题。主要研究内容和结果如下：（1）研究了复杂网络化动态系统的能控/能观性问题。提出了研究时序网络的理论框架，创新性的采用连续时间切换系统的理论方法，将时序网络转化为时空上演化的网络切片，从三个基本方面深入探讨了时序网络系统控制问题；（2）深入研究复杂网络化动态系统的分布式协调问题。通过设计分布式协议，分别研究了几类复杂网络化动态系统的（有限时间）一致性、包围控制、量化一致性等问题，给出分布式协调问题可解的判据准则；（3）研究了复杂网络化动态系统拓扑设计问题。通过设计指标函数，研究了具有领航者的复杂网络化动态系统解决分布式协调问题时的最优/次优拓扑，给出拓扑设计的优化算法；（4）基于演化博弈理论深入研究复杂网络化动态系统中的合作行为。在演化博弈论的框架下，深入研究了合作行为在多人博弈中涌现的理论条件，发现合作行为演化中存在1+1<2 的非常规效应。