变拓扑结构下多智能体系统的追踪问题

发布时间：2018-08-31 12:01

【摘要】：多智能体系统能为规模巨大、个体之间的关系复杂的实际复杂大系统提供很好的建模和控制方式,有着广泛的工业和实际应用潜力。因此,近年来,多智能体协调控制作为复杂系统和控制科学领域的前沿课题被人们关注。由于时变拓扑结构下的非线性多智能体系统极其复杂,研究起来十分困难,所以目前对于多智能体一致性的研究中同时考虑非线性和连续时变拓扑结构的研究成果还不是太多。但是这种系统存在十分重大的实际研究意义,因为大多数的实际系统都含有非线性性质,而且,在智能体运动过程中,各个智能体之间由于速度不同,相对距离会实时变化,由于无线通信距离有限及无线通信本身的不稳定因素等都会引起多智能体之间通信拓扑结构发生实时变化,所以研究非线性多智能体系统在时变拓扑结构下的追踪问题具有十分重要的意义。具体来说,本课题的研究内容主要有以下几个方面：(1)研究一阶、二阶及高阶非线性连续时变拓扑结构下多智能体追踪问题。对移动目标和追踪智能体动力学模型分别为一阶、二阶和高阶非线性模型情况时多智能体系统在连续时变拓扑结构下的一致性追踪问题进行了研究,通过应用图论和矩阵分析的方法,对系统通信拓扑结构的Laplacian矩阵进行分析得到关于其特征值的成功追踪条件。连续时变拓扑结构指多智能体系统的拓扑结构发生连续性变化,而不是在几个固定的拓扑结构之间切换的变拓扑。(2)应用polytopic模型描述连续时变拓扑结构。将时变拓扑结构的Laplacian矩阵应用polytopic模型来表示,即将时变的拓扑结构建模为有限数量的确定Laplacian矩阵和相应的调度函数的组合,该模型的引入使得时变拓扑结构下的多智能体系统追踪策略的存在性转化为线性矩阵不等式的可解性。(3)研究带延时的高阶多智能体系统追踪问题。高阶系统指的是3阶及其以上的系统,例如系统中除了位置、速度、加速度外,还存在急动度。实际系统中多个智能体之间传输信息通过无线通信,传输需要一定时间,甚至出现传输失败,这导致了延时的出现。所以带延时的高阶系统的多智能体系统研究具有很实际的意义。研究中发现,延时的存在不一定就会降低系统的性能,若能设计合适的控制器,保证系统稳定性,延时可能反而改善系统性能,缩短智能体系统的追踪时间,即相对于无延时的系统,追踪智能体在更短的时间内成功追踪到了目标智能体。(4)将滑模控制器引入多智能体系统,缩短在时变拓扑结构下的追踪时间。追踪时间的长短是多智能体系统追踪问题中很关键的性能指标,缩短追踪时间是设计控制器时需要考虑的重要问题。滑模控制技术应用于非线性系统的控制器设计,在许多应用中取得了良好的控制效果。故将其应用于时变拓扑结构的多智能体系统控制中,设计出相关的时变滑模控制器,仿真验证了多智能体滑模控制器的控制效果,对比常规控制器,滑模控制器的应用缩短了追踪时间,提高了追踪效果。(5)基于Voronoi图分割区域多智能体系统目标接力追踪问题。研究了多目标情况下多智能体的追踪问题,假设在某一特定区域内设置许多智能体节点,保证该区域中每一块区域都能同时被至少3个智能体监控,以能够实现目标定位。然后根据Voronoi图的理论将被监控区域分为众多Voronoi单元,当目标进入不同、Voronoi单元时追踪智能体进行切换,即实现对目标智能体的接力追踪。智能体的变换不仅带来了拓扑结构的切换而且引起了追踪误差的跳变,致使稳定性的分析更加复杂。另外,还研究了基于Voronoi图分割区域的具有不稳定子系统的接力追踪问题。研究事件触发的切换拓扑结构多智能体系统出现不稳定子系统的情况。多智能体系统在追踪过程中,通信拓扑结构发生变化,拓扑结构不能够保证每一时间段的追踪子系统都是稳定的,如何设计控制器以及当切换频率和不稳定子系统持续时间满足什么条件时能够保证整体追踪系统的稳定性是具有挑战性的问题。最后,归纳总结本文的主要结果,并对今后的工作进行展望。
[Abstract]:Multi-agent systems can provide a good modeling and control method for large-scale, real complex systems with complex relationships between individuals, and have a wide range of industrial and practical potential. Therefore, in recent years, multi-agent coordinated control as a frontier subject in the field of complex systems and control science has been concerned. Nonlinear multi-agent systems under structures are extremely complex and difficult to study. So far, there are not many researches on the consistency of multi-agent systems which consider both nonlinear and continuous time-varying topologies. In addition, the relative distance between the agents will change in real time because of the different velocities in the process of the agents'movement. Because of the limited wireless communication distance and the instability of the wireless communication itself, the communication topology between the agents will change in real time, so the nonlinear multi-agent is studied. It is very important to study the tracking problem of multi-agent systems under time-varying topology. Specifically, the main contents of this paper are as follows: (1) To study the multi-agent tracking problem under first-order, second-order and high-order nonlinear continuous time-varying topology. The dynamic models of moving targets and tracking agents are first-order and second-order, respectively. Consistency tracking of multi-agent systems under continuous time-varying topology is studied in the case of order and higher-order nonlinear models. By using graph theory and matrix analysis, the Laplacian matrix of system communication topology is analyzed to obtain the successful tracking conditions for its eigenvalues. The topology of a multi-agent system changes continually rather than switching between several fixed topologies. (2) The continuous time-varying topology is described by using the polytopic model. The Laplacian matrix of the time-varying topology is represented by the polytopic model, and the time-varying topology is modeled as a finite number of veracities. The Laplacian matrix and the corresponding scheduling function are combined. The introduction of this model makes the existence of the tracking strategy of multi-agent systems under time-varying topology be transformed into the solvability of linear matrix inequalities. (3) The tracking problem of high-order multi-agent systems with delay is studied. In addition to position, velocity and acceleration, there is also a degree of urgency in the system. In the actual system, the transmission of information between multiple agents through wireless communication takes a certain amount of time, even transmission failure, which leads to the emergence of delay. Therefore, the study of multi-agent system with delay is of great practical significance. Nowadays, the existence of delay does not necessarily degrade the performance of the system. If a suitable controller can be designed to ensure the stability of the system, the delay may improve the system performance and shorten the tracking time of the agent system, that is, compared with the system without delay, the tracking agent can successfully track the target agent in a shorter time. (4) Sliding mode control The tracking time is a key performance index in the tracking problem of multi-agent system. It is an important problem to shorten the tracking time when designing the controller. Sliding mode control technology is applied to the controller design of nonlinear systems, and many applications are needed. Good results have been achieved in the application. Therefore, it is applied to the multi-agent system control with time-varying topology, and the time-varying sliding mode controller is designed. The control effect of the multi-agent sliding mode controller is verified by simulation. Compared with the conventional controller, the application of the sliding mode controller shortens the tracking time and improves the tracking effect. Target relay tracking problem of multi-agent system with Voronoi map partitioned region is studied. The multi-agent tracking problem in multi-target situation is studied. It is assumed that many agent nodes are set up in a specific region to ensure that each region in the region can be monitored by at least three agents at the same time, so as to achieve target location. The theory of noi diagram divides the monitoring area into many Voronoi units. When the target enters different Voronoi units, the tracking agent switches, that is, realizing the relay tracking of the target agent. In addition, the problem of relay tracking with unstable subsystems based on Voronoi graph is studied. The unstable subsystems of multi-agent system with event-triggered switching topology are studied. Tracking subsystems are stable. It is a challenging problem to design controllers and to ensure the stability of the whole tracking system when the switching frequency and the duration of the unstable subsystems are satisfied.
【学位授予单位】：北京理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP18;TP13

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