【作者】 张文涛；

【导师】 左志强；

【作者基本信息】 天津大学 ， 控制理论与控制工程， 2020， 博士

【摘要】 多智能体系统在智能交通、智能电网、航空航天、机器人、无线传感网络等领域具有广泛的应用。协同控制使得智能体状态在集体层面上实现趋同,进而完成单个智能体无法完成的任务。本文结合国内外多智能体系统协同控制最新成果,研究了敌对与协作信息下多智能体系统的协同控制问题,并将其拓展到基于多智能体系统框架的社交网络舆论动力学和隐私保护问题。本文的主要工作总结如下:首先,提出了敌对信息下一阶多智能体系统的协同控制算法。控制协议中的松弛参数表征智能体间交互信息敌对与否,而加权增益保证了系统的收敛性。从理论上证明了加权增益的存在性,给出了系统矩阵特征值位于单位圆内且1特征值重数为1的判据。通过线性变换避免全局信息的使用,建立误差系统与原系统的关系,给出系统协同控制的条件。在上述工作的基础上,研究了领导者-跟随者和时变拓扑下具有敌对信息的协同控制问题,详细分析和探讨了所提算法和Altafini模型之间的关系。其次,研究速度和通信受限下二阶多智能体系统的协同控制问题。针对一般有向图,证明了协同控制与系统的拓扑结构和加权系数相关。为进一步降低通信负担,设计了基于事件触发和基于量化的事件触发机制下二阶多智能体系统协同控制协议。为避免全局信息,接着研究了基于节点和边的协同控制问题,给出相应的判定条件,推广了固定通信拓扑下二阶多智能体系统协同控制的结论。针对二阶多智能体系统,研究其敌对信息下的协同控制问题。由于速度和位置对应的松弛变量通常不具有相关性,与一阶系统和协作信息交互下二阶系统相比,敌对信息下二阶多智能体系统协同控制问题更具挑战性。证明了加权增益的存在性,给出系统矩阵有且仅有两个零特征值且非零特征值具有负实部的判据。讨论了两种特殊情形下敌对二阶多智能体系统的协同控制问题,建立了相应的协同控制判据。针对一般线性多智能体系统,研究敌对信息下的协同控制问题,给出系统协同控制判据以及智能体最终收敛值。对于智能体状态不能直接获得的情况,基于输出信息,设计了分布式观测器,保证智能体实现协同的同时观测误差收敛到零;分析了系统的协同控制区域。考虑输入饱和与敌对信息共同作用下一般线性多智能体系统的半全局协同控制问题,利用低增益反馈给出相应的判据。随后,拓展敌对信息下多智能体系统框架,研究基于多智能体系统的社交网络舆论动力学。引入评估网络刻画个体对邻居个体观念的认知取向,即敌对或信任;利用交互网络表征个体间的交互机理。研究表明协作的评估网络导致观念一致性,而敌对的评估网络则形成观念群分。详细分析了协作、敌对评估网络和观念一致性之间的关系。利用随机凸优化方法,给出先验约束下估计评估网络所需的采样下界。将上述结果推广到多问题关联约束的情形,给出观念一致性、群分和稳定的判据。最后研究多智能体系统的隐私保护问题。基于最小能观子空间,证明加入适当的噪声可以实现智能体初始值的隐私保护。提出基于节点的隐私保护机制,指出只要给超过半数的节点加入噪声即可实现系统隐私保护。进一步给出基于边的隐私保护机制,证明在这种情况下即使少于半数的节点引入噪声,也能实现隐私保护,这在一定程度上揭示了系统隐私保护水平和复杂度之间的折中。更多还原

【Abstract】 Multi-agent systems have a wide range of applications in areas such as intelligent transportation,smart grid,aerospace,robotics and wireless sensor networks,etc.Coordination control enables agent states to aggregate a common value at the collective level,thereby completing tasks that cannot be handled by a single agent.This thesis,incorporating with the state-of-the-art results on coordination of multi-agent systems,is dedicated to investigating the cooperative control problems of multi-agent systems in the presence of both antagonistic and cooperative information.The deduced results are further extended to quantify the opinion dynamics in social network and the privacy preserving within the framework of multi-agent systems.The main contents of this thesis are listed below:First,a coordination algorithm for the first-order multi-agent systems in the presence of antagonistic information is proposed,where the scaling parameter quantifies whether the agent is antagonistic or not,and the weighted gain assures the convergence of the underlying system.The existence of the weighted gain is proved,and a criterion is derived,which guaranteeing that all eigenvalues of system matrix are contained in the unit disk,except for a simple 1 eigenvalue.To avoid the global information,a linear transformation is employed to establish the relationship between the error system and the original system.A coordination condition of the agents subject to antagonistic information is obtained.The derived results are further extended to the scenarios of the leader-follower and the changing interaction topology.Furthermore,the relationship between the above algorithm and Altafini model is elaborated in details.The coordination problem for second-order multi-agent systems without velocity information is then discussed.For general directed graph,it is shown that the underlying coordination problem is tightly linked to communication topology and the weighted gains.To further reduce the communication burden,the coordination protocols using event-triggered and quantization-triggered mechanisms are designed.To circumvent the global information,node-based and edge-based coordination algorithms are developed with the corresponding coordination criteria.Therefore,it generalizes the collaborative control for second-order multi-agent systems under the fixed communication topology.For second-order multi-agent systems,we study the coordination issue with antagonistic interaction.Since the scaling parameters for speed and position are usually not correlated,the cooperative control for second-order multi-agent systems under hostile information is more challenging comparing with the first-order case.We prove the existence of the weighted gain,and give the criterion judging whether there are merely two zero eigenvalues and the nonzero eigenvalues have negative real parts.The proposed setup is further extended to two cases,and the corresponding coordination criteria are presented.For general linear multi-agent systems,the coordination problem in the presence of antagonistic information is suggested to give the coordination condition for the interacting agents.Additionally,the explicit expression of the final aggregated value for each interacting agent is formulated.By using output information of the agents,the distributed observer for the coordination of the participating agents is devised,while guaranteeing the observer error approaches to zero eventually.The underlying coordination region is analyzed in details.Considering the constraint of input,we focus on the semi-global coordination problem via low gain feedback for multi-agent systems subject to both antagonistic information and input saturation.The opinion dynamics of social networks is studied which naturally expands the setup of multi-agent systems with antagonistic interactions.The primary idea is to bring in an appraisal network that quantifies the level of cognitive orientation on the opinions of remaining individuals(i.e.,antagonistic or trust),while the interacting network characterizes the interaction mechanism of the participating individuals in social networks.It is found that cooperative appraisal network leads to consensus in opinions,while antagonistic appraisal network results in clusters in opinions.With the help of random convex optimization,the lower bound on the number of the samples used to estimate the underlying appraisal network with priori constraints is explicitly given.The obtained result is extended to the case of multi-issue interdependence,and the criteria on consensus,clusters and stability of the interacting individuals are presented.Finally,the privacy preserving problem of multi-agent systems is addressed.With the aid of minimum observable subspace,it is proved that adding appropriate amount of noise can achieve privacy preserving of system’s initial value.Based on this argument,the node-based privacy preserving mechanism is put forward and it is pointed out that privacy preserving problem is solvable provided that no less than half of the sensor nodes are blurred by random noise.Furthermore,an edge-based privacy preserving mechanism is given to indicate that privacy preserving is ensured as long as certain conditions are fulfilled,even if less than half of the sensor nodes are disturbed by random noise.This reveals the compromise between the system privacy protection level and the system complexity to a certain extent.更多还原