【作者】 朱振华；

【导师】 关治洪；

【作者基本信息】 华中科技大学 ， 控制科学与工程， 2021， 博士

【摘要】 近年来,广义多智能体系统协同控制因其广泛的工程背景以及在机器人、电力、化工、航空、航天等领域的广阔应用前景,吸引了越来越多国内外控制界学者的关注。相比于正常多智能体系统,广义多智能体系统在结构上更为复杂,且具有诸多新的特性,因而其协同控制问题的研究更为困难且具挑战性。目前,广义多智能体系统的协同控制研究已取得了一些结果,但绝大多数研究结果都是针对智能体间仅存在合作相互作用的广义多智能体系统得到的。然而,在许多实际多智能体系统中,例如生物系统、经济系统、社会网络,智能体之间不仅存在合作的相互作用,也同时存在对抗的相互作用。因此,研究合作与对抗交互并存的广义多智能体系统协同控制问题具有重要的理论和实际意义。本文以领航者–跟随者框架下的线性合作–对抗广义多智能体系统为研究对象,综合运用符号图论、矩阵理论、线性广义系统理论以及多智能体系统协同控制理论相关知识,系统地研究了二分一致性跟踪与二分包含控制问题。主要内容包括:针对具有输入饱和约束的连续时间线性合作–对抗广义多智能体系统,研究了其在固定符号图拓扑下的半全局二分一致性跟踪问题。通过利用基于参量广义代数黎卡提方程的低增益反馈方法,设计了一种基于相邻智能体相对状态的状态反馈控制器和一种基于观测器的反馈控制器。综合运用广义李雅普诺夫函数方法与线性矩阵不等式技术,分析得到了系统实现半全局二分一致性跟踪的充分条件。数值例子验证了所设计控制器的有效性。针对具有多个动态领航者的连续时间和离散时间线性合作–对抗广义多智能体系统,研究了系统在固定符号有向图拓扑下的二分包含控制问题,其中每个领航者可以是自主的,也可以通过与它相邻的领航者交互而动态演化。首先,利用矩阵论和图论有关工具,建立了弱连通符号有向图的Laplacian矩阵与Perron矩阵的一些基本性质。然后,针对连续时间和离散时间两种情形,分别设计了基于相邻智能体相对状态的分布式控制协议,并基于矩阵论与线性广义系统理论相关知识推导出了系统在所提出的控制协议下实现二分包含的充要条件。最后,给出数值仿真验证了所提结果的正确性。针对具有多个动态领航者的连续时间线性合作–对抗广义多智能体系统,研究了其在固定符号有向图拓扑下的基于观测器的二分包含控制问题。利用不同的局部输出信息,设计了三种不同类型的基于观测器的分布式控制协议,并给出了相应控制协议的设计算法。基于矩阵理论和连续广义线性系统理论相关知识,分析得到了保证系统实现二分包含的充分条件。通过数值例子说明了所提出的三种控制协议的有效性。针对具有固定符号有向图拓扑的离散时间线性合作–对抗广义多智能体系统,研究了基于观测器的二分包含控制问题。基于修正的离散广义黎卡提方程方法,使用不同的局部输出信息设计了三种不同的基于观测器的分布式控制协议,并给出了相应控制协议的设计算法。通过利用矩阵理论和离散线性广义系统相关理论,给出了确保系统实现二分包含的充分条件。通过数值仿真验证了所提出控制协议的有效性。针对连续时间和离散时间线性合作–对抗广义线性多智能体系统,研究了系统在固定符号有向图拓扑下的基于降阶观测器的二分包含控制问题。首先,针对连续时间情形,基于连续广义黎卡提方程和广义Sylvester方程方法,设计了一种利用相邻智能体相对输出的基于正常降阶状态观测器的控制协议,并通过理论分析得到了确保系统实现二分包含的充分条件。其次,针对离散时间情形,运用修正的离散广义黎卡提方程和广义Sylvester方程方法,类似地设计了一种使用相邻智能体相对输出的基于正常降阶状态观测器的控制协议,通过理论分析给出了保证系统实现二分包含的充分条件。最后,给出两个数值例子验证了所提出控制协议的有效性。更多还原

【Abstract】 In recent years,coordinated control of generalized multi-agent systems has attracted the attention of more and more scholars in the control field at home and abroad due to its extensive engineering background and broad potential applications in robotics,electricity,chemical engineering,aviation,aerospace and many other areas.Compared with normal multi-agent systems,generalized multi-agent systems are more complicated in structure and have many new characteristics,and hence the study of their coordinated control problem is more difficult and challenging.To data,many results have been obtained concerning the coordinated control of generalized multi-agent systems,yet the overwhelming majority of existing results focus on the generalized multi-agent systems which only include cooperative interactions among agents.However,in many practical multi-agent systems,such as biological systems,economic systems,and social networks,the interactions between agents can be not only cooperative but also antagonistic.Thus,it is of both theoretical and practical significance to study the coordinated control problem of generalized multi-agent systems in which both cooperative and antagonistic interactions coexist.This dissertation is devoted to study the problems of bipartite consensus tracking and bipartite containment control for linear cooperative-antagonistic generalized multi-agent systems in the leader-follower framework,by using tools from signed graph theory,matrix theory,linear generalized system theory,and coordinated control theory of multi-agent systems.The main contents of this dissertation are as follows.The problem of semi-global bipartite consensus tracking for continuous-time linear cooperative-antagonistic generalized multi-agent systems subject to input saturation under fixed signed graph topology is investigated.By exploiting a parametric generalized algebraic Riccati equation(GARE)-based low-gain feedback approach,a state feedback controller relying on the relative states of neighboring agents and an observer-based feedback controller are designed.By using generalized Lyapunov function method and linear matrix inequalities technique,sufficient conditions for the closed-loop system to achieve semi-global bipartite consensus tracking are derived.Numerical examples are given to illustrate the effectiveness of the proposed controllers.The bipartite containment control problem for both continuous-time and discretetime linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under static signed digraph topology is studied,where each leader can be autonomous or dynamically evolving via interactions with its neighboring leaders.First,by using matrix-theoretic and graph-theoretic tools,some fundamental properties for the Laplacian and Perron matrices of weakly connected signed digraphs are established.Then,distributed control protocols based upon the relative states of neighboring agents are designed for both continuous-time and discrete-time cases.In addition,necessary and sufficient conditions ensuring the bipartite containment of the considered multi-agent systems under the proposed control protocols are derived by utilizing tools from matrix theory and linear generalized system theory.Finally,numerical simulations are provided to demonstrate the validity of the proposed results.The problem of observer-based bipartite containment control for continuous-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under static signed digraph topology is investigated.By using different local output information,three different types of distributed observer-based control protocols are proposed.Multi-step algorithms for constructing the corresponding proposed protocols are also given.Based on the matrix theory and continuous generalized linear system theory,sufficient conditions for bipartite containment of the considered systems are obtained.The effectiveness of the three proposed control protocols is demonstrated by numerical examples.The observer-based bipartite containment control problem of discrete-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders under signed digraph topology is studied.In light of the modified discrete-time generalized Riccati equation method,three different distributed observer-based control protocols are designed utilizing different local output information.Meanwhile,algorithms for constructing the corresponding proposed protocols are presented.By using matrix theory and discrete linear generalized systems theory,sufficient conditions to ensure the bipartite containment of the considered generalized multi-agent systems are given.Numerical examples are presented to illustrate the effectiveness of the proposed control protocols.The problem of reduced-order observer-based bipartite containment control for both continuous-time and discrete-time linear cooperative-antagonistic generalized multi-agent systems with multiple dynamic leaders over static signed digraph topology is investigated.In light of the continuous-time generalized Riccati equation and generalized Sylvester equation methods,a distributed normal reduced-order observer-based control protocol relying upon the relative output information of neighboring agents is proposed for the continuous-time case,and sufficient condition is established via theoretical analysis.Furthermore,by using the modified discrete generalized Riccati equation and the generalized Sylvester equation methods,a distributed normal reduced-order observer-based control protocol using the relative outputs of neighboring agents is designed similarly for the discrete time case,and sufficient condition to ensure the bipartite containment of the considered generalized multi-agent systems is derived through theoretical analysis.Finally,two numerical examples are provided to validate the effectiveness of the proposed control protocols.更多还原