符号网络下多智能体系统的群体行为与分布式控制

Research on distributed control of multi-agent systems has been dominantly focused on nonnegative graphs, where all agents cooperate. However, this is not the case for many scenarios, such as social networks and genetic regulatory networks, where competition may exist between agents. In these cases, new collective behaviors emerge, such as bipartite consensus and sign consensus. These cases involve signed graphs, whose adjacency matrix ceases to be nonnegative, posing a challenge for analysis and control of the multi-agent systems. Moreover, multi-agent systems are hardly identical, and most communication networks are time-varying in practice. Therefore, our primary goal in this project is to incorporate conventional control techniques such as neural adaptive control and output regulation, and signed graph theory, into solving two specific consensus problems of both heterogeneous linear and nonlinear multi-agent systems over signed directed graphs. Specifically, we will take a progressive approach and attempt to solve the following two classes of problems: (1) bipartite consensus of heterogeneous linear and nonlinear multi-agent systems; (2) sign consensus of heterogeneous linear and nonlinear multi-agent systems. All these problems are posed over signed switching directed graphs. This research plan is expected to investigate the relationship between bipartite consensus / sign consensus and the conventional consensus, develop graph based Lyapunov stability theory, and produce new tools for design and analysis of multi-agent systems over signed graphs. Observing that signed graphs based multi-agent systems find applications in various scenarios, this research project is believed to hold both considerable academic interests and practical importance.

截至目前，多智能体系统的研究多假设网络中仅存在合作关系。然而在众多应用中，如社会网络和基因调控网络等，某些个体间却是竞争关系。此时，多智能体系统将呈现出新的群体行为，如二分一致性和符号一致性等。因描述个体间关系的网络为符号网络，其邻接矩阵不再是非负矩阵，导致基于非负图的相关结论与分析工具不再适用，从而大大增加了研究难度。另外，时变网络和异质系统更加贴近实际情况，且多数非线性系统中含有未知动态。因此本项目拟将分布式输出调节、神经网络自适应控制等方法与符号图理论相结合，研究以下两大类问题：(1) 切换网络下异质线性系统和动态未知非线性系统的二分一致性问题；(2) 切换网络下异质线性系统和动态未知非线性系统的符号一致性问题。通过以上研究，发展基于符号网络的Lyapunov稳定性理论，提出适用于符号网络的多智能体系统的分析工具，为符号网络下多智能体系统群体行为和控制的进一步研究提供可行的解决方案。

截至目前，多智能体系统的研究多假设网络中仅存在合作关系。然而在众多应用中，如社会网络和基因调控网络等，某些个体间却是竞争关系。此时，多智能体系统将呈现出新的群体行为，如二分一致性和符号一致性等。因描述个体间关系的网络为符号网络，其邻接矩阵不再是非负矩阵，导致基于非负图的相关结论与分析工具不再适用，从而大大增加了研究难度。另外，时变网络和异质系统更加贴近实际情况，且多数非线性系统中含有未知动态。本项目主要研究了：(1) 结构平衡符号图下线性多智能体系统的二分一致跟踪问题，同时考虑了同质系统和异质系统，验证了该问题和传统一致跟踪问题的等价性；(2) 结构平衡符号网络下非线性多智能体系统的二分一致性问题，考虑了执行器具有迟滞特性的非线性系统和系统的瞬态性能；(3) 结构不平衡符号网络下线性多智能体系统的状态符号一致性问题，分别考虑了同质系统和异质系统，考虑了固定拓扑和切换拓扑的情况，给出了符号图联合最终正的概念；(4) 异质线性系统的输出符号一致性问题，考虑了存在领导者和不存在领导者的两种情况；(5) 有向符号图下多智能体系统的能控性问题，给出了能控性条件；(6) 符号图下含有未知扰动的异构拉格朗日系统的符号一致性问题，考虑了不存在领导者的情况；(7) 基于数据的线性多智能体系统的优化问题，利用一种强化学习的技术，即Q-learning技术，解决了异质线性系统的优化跟踪问题；(8) 直流微电网的电压协调和电流分配协同控制问题，同时考虑了系统的信息层和物理层的耦合，为每个分布式电源设计了分布式控制器，使得电压调节和电流分配两个目标可以同时实现；(9) 同构线性多智能体系统跟踪控制的瞬态性能问题，设计了一种分布式控制器，可以对系统的极点进行配置，进而影响到系统的瞬态性能。通过以上研究，进一步发展了基于符号网络的系统分析理论，提出适用于符号网络的多智能体系统的分析工具，为符号网络下多智能体系统群体行为和控制的进一步研究提供可行的解决方案。.