【作者】 林琳；

【导师】 董久刚；

【作者基本信息】 哈尔滨工业大学 ， 运筹学与控制论， 2016， 硕士

【摘要】 多智能体系统在实权网络中的一致性问题在一些文献中已经有所研究。复值系统能够应用于模拟包括复值信号和飞机运动在内的许多现象,从而自然的出现了一个问题:在某种意义上我们是否能够在复权网络中建立一致性。对此,本文给出了肯定的答案。更确切的说,本文给出了复权网络中所有智能体能够实现模一致即所有智能体达到相同的模。第二章给出了本文所使用的一般记号以及关于复权图的定义。给出了有向图的Laplacian矩阵特征值的性质。然后,给出了受扰动的Laplacian矩阵特征值的性质与其相应有向图的连通性之间的关系。最后,给出了复权图中的对角均等矩阵Hurwitz稳定的充分必要条件。第三章给出连续时间和离散时间下模一致的充分必要条件,明确揭示了网络的连通性和复权的结构性质如何共同地影响模一致性。为实现任意形状编队给出了比例一致的概念及系统实现比例一致的条件。作为一个特殊情况,得到了符号图上的二分一致的结果。第四章主要将模一致性结果应用于智能体系统平面上的圆形编队。首先给出了具有相对位置圆形编队的定义,即需要所有的智能体收敛到以给定点为圆心的公共圆且智能体间按指定的角度间隔和顺序排列成期望的形式。得到的主要结果为具有相对位置的圆形编队能够实现当且仅当有向通信图有一个生成树。但它的半径和绝对位置并不确定。为了完全决定一个圆形编队,接着给出了具有绝对位置圆形编队的控制。应用牵制控制方法,发现绝对位置的圆形编队能够通过单一的局部控制器实现当且仅当有向通信图有一个生成树。更多还原

【Abstract】 Consensus problems for multi-agent systems in the literature have been studied under real weighted networks. Complex-valued systems can be used to model many phenomena in applications including complex-valued signals and the motion in a plane.A natural question that arises is whether we can establish consensus under complex-weighted networks in some sense. In this paper, we provide a positive answer to this question. More precisely, we give that in a complex-weighted network all agents can achieve modulus consensus in which the states of all agents reach the same modulus.The second chapter gives some general notations used in this paper, as well as definition of the complex-weighted digraph. We give the properties of eigenvalues of the Laplacian matrix in terms of its associated digraph. Then, we give the relationship between the properties of eigenvalues of the perturbed Laplacian matrix and the connectivity of its associated digraph. Finally, his chapter gives the necessary and sufficient condition for Hurwitz stability of diagonally equiptent matrices in complex weighted networks.The third chapter gives the necessary and sufficient conditions for modulus consensus in both continuous-time and discrete-time cases, which explicitly reveal how the connectedness of networks and structural properties of complex weights jointly affect modulus consensus. This chapter, to achieve arbitrary shaped formation, gives scaled consensus under complex weighted networks. As a special case, the necessary and sufficient conditions for bipartite consensus on signed networks are obtained.The fourth chapter mainly uses the modulus consensus results to achieve circular formation in a plane. We first give the definition of circular formation with relative positions that requires all the agents converge to a common circle centered at a given point and are distributed along the circle in a desired pattern, expressed by the prespecified angle separations and ordering among agents. The main result is the circular formation with relative positions can be achieved if and only if the communication digraph has a spanning tree. However, it has the unspecified radius and absolute phases. To completely determine the circular formation, we give the control problem of circular formation with absolute positions. By using the pinning control strategy, we find that the circular formation with absolute positions can be achieved via a single local controller if and only if the communication digraph has a spanning tree.更多还原