文献类型：期刊文献

中文题名：基于非线性波方程的可变输入时滞多智能体系统编队控制

英文题名：Nonlinear Wave Equation-Based Formation Control for Multi-Agent Systems with Time-Varying Input Delay

作者：钟佳岐 陈修顺 曾诚

第一作者：钟佳岐

机构：[1]重庆邮电大学自动化学院,重庆400065;[2]贵州理工学院理学院,贵阳550003

第一机构：重庆邮电大学自动化学院,重庆400065

年份：2026

卷号：46

期号：3

起止页码：756-772

中文期刊名：系统科学与数学

外文期刊名：Journal of Systems Science and Mathematical Sciences

收录：;北大核心:【北大核心2023】；

基金：国家自然科学基金(62003066,62163008);重庆市自然科学基金(cstc2021jcyj-msxmX0331,CSTB2025NSCQGPX1256);贵州省科技厅重点项目(黔科合基础[2020]1Z054)资助课题。

语种：中文

中文关键词：多智能体;可变输入时滞;编队;非线性波方程;分段控制

外文关键词：Multi-agent system;time-varying input delay;formation;nonlinear wave equation;piecewise control

摘要：为了解决具有可变输入时滞的大规模二阶多智能体集群编队控制问题,文章提出了一种基于状态观测器的局部分段控制策略.首先,基于链式拓扑结构特征以及期望位置信息,反向运用差分策略,将离散多智能体连续化,推导出含阻尼的二阶波方程模型等效替代传统且繁琐的常微分方程组(ordinary differential equations,ODEs);其次,围绕可变输入时滞的固有约束,考虑领导者与跟随者的交互机制,构建具有时滞补偿特征的误差状态观测器;再次,基于估计的领导者动力学特性,提出分段局部控制策略,并在线性矩阵不等式(linear matrix inequality,LMI)的框架下,融合Lyapunov-Krasovskii函数、Writinger不等式的变式、Jensen不等式以及Halanay不等式,推导出能够保证误差系统稳定的充分条件;最后,分别在二维与三维空间进行对比仿真,成功验证所提出编队控制方法的有效性.
This paper investigates the problem of formation control for a largescale agent cluster with a chain topology and time-varying input delay.In contrast to previous contributions,the multi-agent system is mathematically modeled using a nonlinear second-order wave equation,and an observer-based piecewise controller is proposed to collaborate the leader-following agents.Firstly,from the continuum perspective of chain topology,a wave equation is derived by employing the reverse application of spatial difference method as a substitution for the cumbersome ordinary differential equations;Subsequently,an error state observer is proposed to effectively address the time-varying input delay and accurately estimate the actual positions of leader agents;Then,within the framework of Linear Matrix Inequality(LMI),the suffcient conditions for a piecewise controller are derived by integrating the Lyapunov-Krasovskii function,a variant of Writinger’s inequality,Jensen’s inequality and Halanay’s inequality;Finally,the effectiveness of proposed formation controller are demonstrated through two comparative simulations conducted in both 2D and 3D spaces.