可变脉冲控制下的多智能体系统固定时间一致性研究

Research on Fixed-Time Consensus of Multi-Agent Systems via Variable Impulsive Control

为降低网络节点间的通信成本并提升系统收敛速度,提出基于可变脉冲控制的多智能体系统(MASs)固定时间一致性的双阶控制(TSC)策略。将整个控制周期分为可变脉冲控制阶段和固定时间连续控制阶段,根据实际应用需求动态调整脉冲控制和固定时间控制的时间周期,并且在脉冲时间窗内可随机进行脉冲采样。采用固定时间一致性理论使MASs的一致性时间不依赖于系统的初始条件,引入随机扰动增强TSC策略在实际系统中的可用性,利用Lyapunov函数、代数图论和矩阵分析得到系统达到固定时间一致性的充分条件。通过具有切换拓扑结构的领导-跟随者数值仿真案例验证了理论分析的有效性,并表明TSC策略的收敛时间和通信次数相比于单一可变脉冲控制和单一固定时间连续控制分别减少了0.07 s和6~9。

This study proposes a Two-Stage Control(TSC) strategy with fixed-time consensus for Multi-Agent Systems(MASs) with stochastic disturbances via variable impulsive control theory to reduce communication costs between nodes and improve the convergence rate of the system. The TSC strategy divides the entire control period into two parts:variable impulsive control and fixed-time consensus control.The TSC can dynamically adjust the time periods of these stages according to practical application requirements,and the impulsive sampling in the TSC strategy occurs randomly within an impulsive time window. The settling time for the MASs is independent of the initial conditions applied by the fixed-time stability. In addition,by introducing stochastic disturbances present in actual scenes into the MASs,this control strategy is significantly reliable in real systems.The Lyapunov function,algebraic graph theory,and matrix analysis are applied,and sufficient conditions for the system to achieve a fixed-time consensus are obtained.Finally,a numerical simulation example of the leader-follower case with switching topology is used to demonstrate the validity of the theoretical analysis. The simulation results show that the convergence time of the TSC strategy is 0.07 s shorter than that of a single variable pulse control.Moreover,the number of communications is 6-9 times less than that of a single fixed-time continuous control.