摘要
多Agent系统的研究工作在最近十几年得到了全面的展开,本论文从控制理论的角度对多Agent系统的控制及稳定性分析等问题进行了研究,主要内容如下:
(1)研究了人工势场方法对多Agent系统进行控制的问题。在二维环境中以二次积分模型为研究对象,基于电势场的相关概念提出人工势场函数,并推导出由此产生的各个Agent之间及Agent和障碍物之间的力,同时结合比例-微分控制使整个系统在保持队形的同时能够避开障碍物并朝目标前进。通过Lyapunov稳定性分析得出系统是稳定的;在此控制策略的基础上,提出虚拟改进障碍物外部形状的方法,使得各Agent能避开由障碍物外形包围而成的局部极小值区域顺利到达目的地。
(2)利用滑动模型方法结合人工势场及图论的知识研究了在三维空间中多Agent系统的轨迹跟踪控制。滑动模型控制方法不受空间维数的限制,同时具有很好的鲁棒性,这恰好能满足多Agent系统的控制要求,因此发挥滑模控制的优势结合人工势场方法和图论对多Agent系统进行控制能有效完成障碍物环境中多Agent系统的轨迹跟踪控制,并能在跟踪过程中满足一定的队形要求,通过选取适当的Lyapunov函数证明了其稳定性。
(3)研究了多Agent系统的稳定性问题。提出了输入-状态弦稳定性(Input-to-State String Stability)的概念,用于分析“弦”结构的稳定性能。这种“弦”结构常作为基本构成单位出现在多Agent系统中。将“弦”中各子系统之间的相互影响看作对子系统的一种输入,并结合输入-状态稳定性、弦稳定性的概念以及奇异摄动理论的分析方法对此类多Agent互联系统的输入-状态弦稳定性进行了分析,给出了弱关联条件下Agent状态交互影响时系统输入-状态弦稳定的充分条件。
(4)研究了多Agent系统的队形变换问题。指出了多Agent系统队形变换的几种形式,利用图论中的连通性、刚性等性质,以及图的相关矩阵对多Agent系统的结构进行分析,从而给出了基于图论方法的队形变换时的控制算法,并给出了由较大图分解成较小子图和两个较小子图合并成大图两种算法的流程。
The research of multi-agent systems has gained great interests during the last decade, the problem of related control theory are studied in this dissertation, such as control law and stability analysis. The main research works are concluded as follows:
(1) The control law and stability analysis with artificial potential field are studied. In two dimension circumstance based on the double integrator mathematic model, a new set of potential functions are presented by referring the concepts of electric field, then a new formation control method is proposed, in which the potential functions are used between agent-agent and between agent-obstacle while Proportional -Differential control is applied for multi-agent system and its goal. Stability of this method is proven. Then a reformative planning strategy is proposed for path planning. This strategy is aimed at a class of local minima which are formed by the obstacle surrounding, this will help reduce the paths of agents and improve the control efficiency. The stability of the original system is kept.
(2) A new sliding mode control strategy of multi-agent systems is studied in three dimensions. Sliding mode control is with no limitation of dimension and has good robustness. The method proposed in this paper is based on sliding mode control combined with artificial potentials and graph theory. It can be widely used to deal with the nonlinear plant in three dimensional spaces, it also can track moving goals or set positions robustly with obstacles in circumstances while keep formation. The stability of the control strategy is proven by choosing proper Lyapunov function.
(3) The stability of multi-agent system is studied. A new definition of Input-to-State String Stability is proposed, mean to analyze the string stability from the input-to-state view. String is a basic structure of many multi-agent systems. By viewing the interconnection as a kind of input to subsystems, sufficient conditions of string stability for a class of weak interconnected nonlinear systems are deduced, which is based on the input-to-state stability analysis and singular perturbation theory.
(4) The method of formation change is studied. Different change forms are classified. The multi-agent system structure can be figured by graph. Some properties of formation can be achieved by analyzing the connectivity, rigid or matrix of relative graphs. The relationship of different agents changes according to the variety in environment. The control arithmetic of reform and split for multi-agent stracture are considered based on the graph theory.
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