基于ODE-PDE的大规模多智能体系统有限时间编队  

Finite-time Formation of Large-scale Multi-agent Systems Based on an ODE-PDE Approach

作　　者：满景涛 曾志刚[1,2] 盛银[1,2] 来金钢 MAN Jing-Tao;ZENG Zhi-Gang;SHENG Yin;LAI Jin-Gang(School of Artificial Intelligence and Automation,Huazhong University of Science and Technology,Wuhan 430074;Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China,Wuhan 430074)

机构地区：[1]华中科技大学人工智能与自动化学院,武汉430074 [2]图像信息处理与智能控制教育部重点实验室,武汉430074

出　　处：《自动化学报》2025年第3期631-642,共12页Acta Automatica Sinica

基　　金：国家重点研发计划(2021ZD0201300);国家自然科学基金(U1913602,61936004,624B2058);国家自然科学基金创新群体项目(61821003);111计算智能与智能控制项目(B18024);中央高校基本科研业务费(2023JYCXJJ010)资助。

摘　　要：现有基于偏微分方程(Partial differential equation,PDE)的多智能体系统(Multi-agent system,MAS)编队控制方法要求智能体必须是密集分布的,为打破这一限制,提出一种新的基于常微分−偏微分方程(Ordinary differential equation-partial differential equation,ODE-PDE)的分析方法,以解决稀疏−密集混合分布的大规模异构MAS编队问题.首先,通过设计特定的通信协议,并基于空间离散系统部分连续化方法,将原始大量的异构MAS的ODE动力学模型转化为由一个PDE和少数几个ODE耦合而成的ODE-PDE模型.为更符合实际复杂场景,将拓扑权值规定为半马尔科夫切换的,且稀疏分布和密集分布智能体遵循不一致的切换规则.其次,针对无时滞和有时滞两种情形,设计两种异步边界控制策略,利用Lyapunov方法得到保证误差系统实际有限时间稳定的充分条件,并得到停息时间和稳定阈值的计算规则.最后,两个广义的数值仿真进一步验证了所提方法的有效性.The existing formation control methods of multi-agent systems(MASs)based on partial differential equation(PDE)require that agents must be densely distributed.To break this limitation,this paper proposes a novel analysis method based on ordinary differential equation-partial differential equation(ODE-PDE),such that the formation problem of large-scale heterogeneous MASs with sparse and dense mixed distribution could be solved.First,the original numerous heterogeneous ODE dynamics models of MASs are transformed into an ODE-PDE model consisting of a PDE coupled to several ODEs through specific communication protocol design and partial continuum method of spatial discrete systems.To match realistic complex scenes better,the topological weights are designed to be semi-Markov switched,and the switching rules followed by sparsely and densely distributed agents are inconsistent.Second,two asynchronous boundary control strategies are designed for delay-free and time-delayed cases,respectively.The Lyapunov method is used to obtain sufficient conditions to ensure the practically finite-time stability of the error system,and the calculation rules of the settling time and stability threshold are provided.Finally,two generalized numerical simulations further verify the effectiveness of the proposed approach.

关 键 词：大规模异构多智能体系统 常微分−偏微分方程 实际有限时间编队 半马尔科夫切换拓扑 异步边界控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TP18[自动化与计算机技术—控制科学与工程]