多智能体系统协调控制中的若干问题研究
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摘要
近年来，多智能体或多主体系统分布式协调控制问题已持续成为国内外不同学科领域研究者的关注点，这是由于其在社会、工业、建设和国防等领域有着广泛的应用背景，如：无人驾驶飞机编队控制、多智能体群集运动、分布式传感器网络、人造卫星群位姿调整及交通拥塞控制等。在多智能体系统协调控制中，一个重要的问题是多智能体系统的一致性控制。所谓一致性问题，简单的说就是随着时间的变化，多智能体系统中各主体之间通过通信协调使所有智能体的状态最终趋于一致。在整个合作过程中，分布式控制协议的设计成为实现全局协同行为的至关重要的因素。
本文的课题得到了国家自然科学基金(61174070)、国家自然科学基金-广东省联合基金重点项目（U0735003）、海外及港澳合作基金(60828006)和高校博士点基金（20110172110033）的部分资助。本文结合代数图论、矩阵理论及Lyapunov稳定性定理，采用理论分析和数值仿真相结合的方法，对网络具有通信时延、测量噪声和变化网络通信拓扑的连续时间多智能体系统协调控制中的两个基本问题进行了研究，即一致性和聚集控制问题。具体的研究内容包括以下几个方面：
第一部分（即第一章和第二章），首先介绍了多智能体系统分布式协调控制的研究背景和意义，其次阐述了多智能体系统协调控制中的基本问题和研究进展。最后就本文的主要工作、所用到的符号及代数图论等预备知识作了必要的说明。
第二部分，研究了通信时延影响下的连续时间多智能体系统静态和动态聚集控制问题。（第三章）首先对于一阶静态聚集控制，利用代数图论和Lyapunov技术，以线性矩阵不等式的形式给出了实现静态聚集控制的时滞相关型判据。并且该结果可以利用MATLAB工具箱LMI Toolbox方便求解。此外，将结果推广到含有通信时延和测量噪声的情形。其次，对于二阶动态聚集控制，利用代数图论、频域分析方法及Nyquist稳定性判据，得到了每个跟随者最终进入动态领导者组成的凸形区域的充分条件。再次（第四章）分别研究了没有通信限制和通信时延干扰下的连续时间分数阶系统的静态聚集控制问题。理论结果表明：只要智能体之间的通信时延不超过给定的最大的时延上界，最终每个跟随者都能够进入多领导者组成的凸多边形区域。最后，数值仿真验证了文中结果的正确性。
第三部分（第五章）研究了连续时间多智能体系统的一致性跟踪控制问题。首先，讨论了具有测量噪声的连续时间二阶积分多智能体系统的一致性跟踪控制，每个跟随者当前时刻接收到的邻居位置状态和速度状态均受到高斯白噪声的干扰。为了减少噪声的影响，引入了一个时变递减的一致性增益。利用速度分解技巧和随机Lyapunov分析方法，得到了闭环系统均方稳定的充分条件。此外，将结果推广到时变通信网络情形。其次，研究了通信时延影响下的高阶多智能体系统有限时间一致性跟踪控制问题。根据泛函微分方程稳定性定理，证明了所有的跟随者都能够在有限时间内跟踪上动态领导者。最后，数值仿真验证了文中所提算法之有效性和可行性。
第四部分（第六章）研究了多个时变通信时延和外界噪声干扰下的连续时间多智能体系统H∞一致性控制问题。每个智能体只能利用自己局部状态信息和接收到的含有不同的通信时延邻居状态信息来更新自己的状态。为了便于分析，利用模型变换将原来的闭环系统转化为一个与之等价的降阶子系统。基于线性矩阵不等式方法和Lyapunov稳定性定理得到了降阶子系统稳定的充分条件。理论结果表明：最终所有智能体系统均达到一致并满足期望的H∞性能。此外，还讨论了变化通信网络拓扑情形下的鲁棒H∞一致性问题。最后，数值仿真表明结果的正确性。
In recent years, the distributed cooperative control of multi-agent systems has at-tracted a considerable interest in various scientific communities due to broad applicationsin social, industrial, construction and national defense areas, such as unmanned air vehi-cles formation control, flocking/swarming, distributed sensor network, attitude alignmentof clusters of satellite and trafc congestion control, and so on. An important problemin distributed coordinated control of multi-agent system is the consensus control. Theso-called consensus problem means to reach an agreement on certain quantities of interestthrough the local communications. The key factor of distributed control of multi-agentsystems is to design a proper distributed control protocol.
This work was supported by the National Natural Science Foundation of China un-der Grant No.61174070, the NSFC-Guangdong Joint Foundation Key Project underGrant No. U0735003, the Oversea Cooperation Foundation under Grant60828006andthe Specialized Research Found for the Doctoral Program No.20110172110033. In thisdissertation, based on the algebraic graph theory, matrix theory as well as Lyapunovstability theory, consensus problem and aggregation problem under time-dependent com-munication channels, measurement noises and switching topologies are investigated bycombining theoretical analysis and numerical simulation methods. This paper includesthe following four aspects:
In the first part (Chapter1and Chapter2), the research background and meaningof the coordinated control of multi-agent systems are firstly introduced briefly. Secondly,the basic problems and some advances in coordinated control are recalled. Finally, themainly work of this dissertation, the used notations and some preliminaries are listed.
In the second part (chapter3), the static and dynamic aggregation control prob-lem of continuous time multi-agent systems with delay-dependent communications arestudied. Firstly, for the first-order static aggregation control problem, by employing al-gebra graph theory and Lyapunov technology, a delay-dependent criterion is establishedin the form of linear matrix inequalities (LMIs). And this result can be easily solved byusing LMI Toolbox in MATLAB. In addition, the results have been extended to com-munication channels containing time delay and measurement noises cases. Secondly, for second-order dynamic aggregation control problem, by combining the tools of algebragraph theory, the frequency domain analysis method and the Nyquist stability criterion,sufcient conditions for the whole follower-agents aggregated in a polytope region formedby the leaders are derived. Thirdly (chapter4), the static aggregation control problemsof fractional-order systems under time delay are discussed. It is shown that each followereventually can enter the convex region which is spanned by the leaders as long as thecommunication delay can not exceeds the maximum bound. Finally, numerical examplesare given for illustration.
In the third part (from chapter5), the distributed tracking control problems ofcontinuous time multi-agent systems are investigated. First of all, a tracking controlproblem of continuous time second-order multi-agent systems under measurement noisesis discussed. The control input of each follower agent can only use its local states and theposition and the velocity states of its neighbors which are all corrupted by Gaussian whitenoises. In order to reduce the influence of the noises, a time-varying and decay consensusgain is introduced. Based on the velocity decomposition techniques and stochastic Lya-punov analysis method, a sufcient condition is obtained, which ensures the relative stateerrors between each follower agent and the active leader converge to zero in the sense ofmean square. In addition, this result is extended to a more general case with switchingtopologies. Moreover, the tracking control problem of high order multi-agent systemswith communication time delay is studied. Based on the functional diferential equationstability theorem, it is shown that the proposed consensus protocol can guarantee thefollowers track the dynamic leader in a finite time. Finally, the numerical simulationresults prove the efectiveness and feasibility of the proposed algorithm.
In the fourth part (chapter6), distributed H∞consensus control problems for con-tinuous time first-order multi-agent systems with multiple time-varying communicationdelays and external disturbances are investigated. Firstly, a model transformation is per-formed, and the original close-loop system is changed into a reduced order system. Then,based on the reduced order system, by constructing a proper delay-dependent Lyapunovfunction and employing LMIs technology, sufcient conditions are derived for all agents toreach an agreement with the desired H∞performance. In addition, this result is extendedto the switching topologies case. Finally, the simulation results show the correctness andvalidity of the theoretical results.
本文的课题得到了国家自然科学基金(61174070)、国家自然科学基金-广东省联合基金重点项目（U0735003）、海外及港澳合作基金(60828006)和高校博士点基金（20110172110033）的部分资助。本文结合代数图论、矩阵理论及Lyapunov稳定性定理，采用理论分析和数值仿真相结合的方法，对网络具有通信时延、测量噪声和变化网络通信拓扑的连续时间多智能体系统协调控制中的两个基本问题进行了研究，即一致性和聚集控制问题。具体的研究内容包括以下几个方面：
第一部分（即第一章和第二章），首先介绍了多智能体系统分布式协调控制的研究背景和意义，其次阐述了多智能体系统协调控制中的基本问题和研究进展。最后就本文的主要工作、所用到的符号及代数图论等预备知识作了必要的说明。
第二部分，研究了通信时延影响下的连续时间多智能体系统静态和动态聚集控制问题。（第三章）首先对于一阶静态聚集控制，利用代数图论和Lyapunov技术，以线性矩阵不等式的形式给出了实现静态聚集控制的时滞相关型判据。并且该结果可以利用MATLAB工具箱LMI Toolbox方便求解。此外，将结果推广到含有通信时延和测量噪声的情形。其次，对于二阶动态聚集控制，利用代数图论、频域分析方法及Nyquist稳定性判据，得到了每个跟随者最终进入动态领导者组成的凸形区域的充分条件。再次（第四章）分别研究了没有通信限制和通信时延干扰下的连续时间分数阶系统的静态聚集控制问题。理论结果表明：只要智能体之间的通信时延不超过给定的最大的时延上界，最终每个跟随者都能够进入多领导者组成的凸多边形区域。最后，数值仿真验证了文中结果的正确性。
第三部分（第五章）研究了连续时间多智能体系统的一致性跟踪控制问题。首先，讨论了具有测量噪声的连续时间二阶积分多智能体系统的一致性跟踪控制，每个跟随者当前时刻接收到的邻居位置状态和速度状态均受到高斯白噪声的干扰。为了减少噪声的影响，引入了一个时变递减的一致性增益。利用速度分解技巧和随机Lyapunov分析方法，得到了闭环系统均方稳定的充分条件。此外，将结果推广到时变通信网络情形。其次，研究了通信时延影响下的高阶多智能体系统有限时间一致性跟踪控制问题。根据泛函微分方程稳定性定理，证明了所有的跟随者都能够在有限时间内跟踪上动态领导者。最后，数值仿真验证了文中所提算法之有效性和可行性。
第四部分（第六章）研究了多个时变通信时延和外界噪声干扰下的连续时间多智能体系统H∞一致性控制问题。每个智能体只能利用自己局部状态信息和接收到的含有不同的通信时延邻居状态信息来更新自己的状态。为了便于分析，利用模型变换将原来的闭环系统转化为一个与之等价的降阶子系统。基于线性矩阵不等式方法和Lyapunov稳定性定理得到了降阶子系统稳定的充分条件。理论结果表明：最终所有智能体系统均达到一致并满足期望的H∞性能。此外，还讨论了变化通信网络拓扑情形下的鲁棒H∞一致性问题。最后，数值仿真表明结果的正确性。
In recent years, the distributed cooperative control of multi-agent systems has at-tracted a considerable interest in various scientific communities due to broad applicationsin social, industrial, construction and national defense areas, such as unmanned air vehi-cles formation control, flocking/swarming, distributed sensor network, attitude alignmentof clusters of satellite and trafc congestion control, and so on. An important problemin distributed coordinated control of multi-agent system is the consensus control. Theso-called consensus problem means to reach an agreement on certain quantities of interestthrough the local communications. The key factor of distributed control of multi-agentsystems is to design a proper distributed control protocol.
This work was supported by the National Natural Science Foundation of China un-der Grant No.61174070, the NSFC-Guangdong Joint Foundation Key Project underGrant No. U0735003, the Oversea Cooperation Foundation under Grant60828006andthe Specialized Research Found for the Doctoral Program No.20110172110033. In thisdissertation, based on the algebraic graph theory, matrix theory as well as Lyapunovstability theory, consensus problem and aggregation problem under time-dependent com-munication channels, measurement noises and switching topologies are investigated bycombining theoretical analysis and numerical simulation methods. This paper includesthe following four aspects:
In the first part (Chapter1and Chapter2), the research background and meaningof the coordinated control of multi-agent systems are firstly introduced briefly. Secondly,the basic problems and some advances in coordinated control are recalled. Finally, themainly work of this dissertation, the used notations and some preliminaries are listed.
In the second part (chapter3), the static and dynamic aggregation control prob-lem of continuous time multi-agent systems with delay-dependent communications arestudied. Firstly, for the first-order static aggregation control problem, by employing al-gebra graph theory and Lyapunov technology, a delay-dependent criterion is establishedin the form of linear matrix inequalities (LMIs). And this result can be easily solved byusing LMI Toolbox in MATLAB. In addition, the results have been extended to com-munication channels containing time delay and measurement noises cases. Secondly, for second-order dynamic aggregation control problem, by combining the tools of algebragraph theory, the frequency domain analysis method and the Nyquist stability criterion,sufcient conditions for the whole follower-agents aggregated in a polytope region formedby the leaders are derived. Thirdly (chapter4), the static aggregation control problemsof fractional-order systems under time delay are discussed. It is shown that each followereventually can enter the convex region which is spanned by the leaders as long as thecommunication delay can not exceeds the maximum bound. Finally, numerical examplesare given for illustration.
In the third part (from chapter5), the distributed tracking control problems ofcontinuous time multi-agent systems are investigated. First of all, a tracking controlproblem of continuous time second-order multi-agent systems under measurement noisesis discussed. The control input of each follower agent can only use its local states and theposition and the velocity states of its neighbors which are all corrupted by Gaussian whitenoises. In order to reduce the influence of the noises, a time-varying and decay consensusgain is introduced. Based on the velocity decomposition techniques and stochastic Lya-punov analysis method, a sufcient condition is obtained, which ensures the relative stateerrors between each follower agent and the active leader converge to zero in the sense ofmean square. In addition, this result is extended to a more general case with switchingtopologies. Moreover, the tracking control problem of high order multi-agent systemswith communication time delay is studied. Based on the functional diferential equationstability theorem, it is shown that the proposed consensus protocol can guarantee thefollowers track the dynamic leader in a finite time. Finally, the numerical simulationresults prove the efectiveness and feasibility of the proposed algorithm.
In the fourth part (chapter6), distributed H∞consensus control problems for con-tinuous time first-order multi-agent systems with multiple time-varying communicationdelays and external disturbances are investigated. Firstly, a model transformation is per-formed, and the original close-loop system is changed into a reduced order system. Then,based on the reduced order system, by constructing a proper delay-dependent Lyapunovfunction and employing LMIs technology, sufcient conditions are derived for all agents toreach an agreement with the desired H∞performance. In addition, this result is extendedto the switching topologies case. Finally, the simulation results show the correctness andvalidity of the theoretical results.
引文
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