离散异构多自主体系统的分布式编队控制

Distributed Formation Control of Discrete Heterogeneous Multi-Agent Systems

针对固定多自主体网络拓扑,研究了离散异构多自主体系统的分布式编队跟踪问题。假设异构多自主体系统由一个领航者、一阶和二阶跟随者自主体构成。首先,不考虑固定时延,针对一阶和二阶跟随者自主体分别设计了分布式编队控制协议,通过利用代数图论及李雅普诺夫稳定理论,得到了所设计的协议有效的充分条件,并以LMI-线性矩阵不等式的形式给出。然后,考虑固定时延,对跟随者自主体设计了相应的编队控制协议,通过构造相应的李雅普诺夫函数,给出了该协议在存在时延时有效的充分条件。理论分析表明,在所设计协议的作用下,跟随者自主体能形成并保持所要求的编队,并且实现了和领航者速度一致。最后,仿真结果亦证明了4个跟随者自主体最终形成了所要求的矩形编队,并且速度与理论分析结果一致,表明了所设计协议的有效性。

In accordance with the fixed multi-agent network topology,the distributed formation tracking of discrete heterogeneous multi-agent system is investigated. Assuming the heterogeneous multi-agent system consists of a leader,first-order follower agents,and second-order follower agents;firstly,without considering the constant time delay,the distributed formation control protocols are respectively designed for the first-order and second-order follower agents,and by using algebraic graph theory and Lyapunov stability theory, the effective sufficient condition of the protocol designed is obtained and given in the form of LMI （ linear matrix inequality） . Then,considering the constant time delay,the relevant formation protocols are designed for the follower agents;through structuring corresponding Lyapunov function, the effective sufficient condition that satisfying protocols with constant time delay is given. The theoretical analysis indicates that under action of the proposed protocols,followers may form and keep the desired formation, and reach consistent speed of the leader. Finally, the simulation results prove that the four agents finally form the desired rectangle formation and reach consistent speed.