基于有向网络的智能群体群集运动控制

Flocking motion control of flock in directed networks

对具有二次积分动态的智能群体(flock/swarm),在有向网络取得群集运动(flocking/swarming)进行了研究．提出了一个分散控制方法对智能群体进行分散控制．用有向图模型表示智能体之间的相互作用及通信关系．对固定的网络拓扑,控制互连拓扑是固定的,时不变的,运用传统的LaSalle不变集原理,代数图论的有关技巧进行了稳定性分析,并得到以下主要结论:i)智能群体速度方向渐进收敛,并保持方向一致;ii)智能群体速度大小渐进收敛,并保持大小相等;iii)有邻接关系的智能体(Agent)之间没有碰撞发生;iv)智能群体的势场函数被最小化．理论分析显示,有向图的弱连通性及一种称为平衡图的有向图在系统的稳定性分析中扮演着关键角色．最后,给出了一个仿真例子对理论结果进行了验证．

Flock with double integrator dynamics to achieve flocking motion formation in directed networks is studied in this paper. A class of decentralized control laws for a flock of mobile agents is proposed. The interaction and/or communication relationship between agents is modeled by directed graph. In fixed network topology, the topology of control interconnection is fixed and time invariant. The stability analysis is achieved by using classical LaSalle＇s invariant principle and the analytical techniques of algebraic graph theory, which results in： i） global alignment of their velocity vectors, ii） convergence of their speeds to a common speed, iii） collisions between interconnected agents avoidance, and iv） minimization of the potential function of flock. Theoretical analysis show that the weak connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in stability analysis. Finally, a simulation example is given to validate the theoretical results.