关于Lur'e型多智能体系统的群一致性研究

The group consensus problem of multi-agent systems is the natural extension and development of the consensus in multi-agent systems. Under complex structure of communication network, group consensus in a class of nonlinear multi-agent systems with Lur'e-type dynamics is investigated in this project. Based on several tools from the stability theory, control theory, algebraic graph theory， matrix theory and absolute stability of Lur'e systems, this project focuses on some practical problems in consensus coordination control of multi-agent systems by means of the combination of time domain and frequency domain method. The main work can be summarized as follows: (1) the group consensus problem with complex communication network; (2) the group consensus problem under uncertainty environmental factors; (3) the group consensus problem of the time-delay systems. Under different structures of communication network, control protocols of group consensus are designed, some conditions are established to realize group consensus of multi-agent systems. In addition, the conception of group consensus region is presented and analysised. The objective of this project can enrich and develop the coordination control theory of multi-agent systems, especially for the study of multi-agent systems with nonlinear dynamics, the understanding of emergency property in biological community and the control of the overall behavior in engineering group.

多智能体系统群一致性问题是多智能体系统一致性问题的自然推广和延伸。本项目研究复杂通讯网络拓扑结构下，具有Lur'e型动态的一类非线性多智能体系统群一致性问题。利用控制论、代数图论、矩阵论以及Lur'e系统绝对稳定性理论等理论和方法，采用时域分析和频域分析相结合的手段，围绕多智能体系统一致性协调控制中的实际问题展开研究。具体包括：（1）复杂的通讯网络结构下系统的群一致性问题；（2）不确定环境下系统的群一致性问题；（3）时延系统的群一致性问题。基于系统的通讯网络拓扑结构，设计局部群一致性控制协议，给出系统实现群一致性的判定条件，刻画并分析群一致性区域概念。本项目的研究结果可丰富和发展多智能体系统协调控制理论，尤其是对于非线性多智能体系统的研究,生物群体涌现性的深入理解以及工程群体的整体行为控制具有重要意义。

多智能体分布式协作问题已成为众多领域研究的热点。本项目主要围绕Lur’e型多智能体系统群一致性问题展开研究，项目整体研究工作分为以下两个方面：（1）针对具有时滞和外部干扰的Lur’e型多智能体系统，基于网络结构，设计相应的控制协议，讨论系统的群一致性问题，利用稳定性的相关理论分析给出多智能体系统实现群一致性的条件，提出群一致性区域的概念。针对分数阶多智能体系统，提出了一种包含现在与过去时间信息的控制协议，讨论系统实现一致性的条件，基于有限时间理论，得到分数阶多智能体系统实现有限时间一致的条件。（2）将多智能体系统研究中分布式协作和网络化的思想应用于生物信息学和电力系统的研究：构建基因共表达网络研究乳腺癌的诊断，利用加权基因共表达网络分析基因表达关联，研究使用乳腺癌细胞系的基因表达分析来预测乳腺癌病人的临床预后，为临床决策提供科学参考。针对在收集蛋白质相互作用网络中存在概率误差和偏倚，研究分析蛋白质相互作用网络中度分布可靠性的影像。基于直流分布式电源系统的多重电容耦合变换器的反馈控制，抑制中间总线和输出中的谐波电压并确保子系统的稳定性。