复杂通信条件下的线性群系统编队控制方法

Formation Control for Linear Swarm Systems with Complex Communication Conditions

针对时变时延和有向切换拓扑两个复杂通信条件,研究了线性群系统的编队控制问题。首先,基于一致性理论,给出了群系统的编队控制协议。其次,利用变量代换,将上述两个复杂通信条件下的群系统编队控制问题,转化为多个时延系统的镇定问题。构造公共Lyapunov-Krasovskii泛函,利用自由权矩阵方法,对时延系统的镇定问题进行分析,得到了保守性较小且适用于大规模系统的线性矩阵不等式(LMI)判据,并求解出时延上界和编队控制器增益。最后,通过数值仿真,对方法的有效性和低保守性进行了验证。

We investigate the formation control for linear swarm systems with complex communication conditions of time-varying delays and switching interaction topologies. Firstly,we propose a formation control protocol based on consensus theory. Secondly,we transform a formation control problem with the two complex communication conditionsinto the stabilization problem of delay-dependent systems using variable substitution. We construct the common Lyapunov-Krasovskii functional and analyze the stabilization problem of delay-dependent systemsby free-weighting matrices method. Then,the linear matrix inequality（ LMI） criterion for largescale swarm systems with lower conservative is obtained. We also give the upper bounds of delays and the controller gain. Finally,we demonstrate the theoretical results and low conservative by numerical simulations.