基于迭代学习算法的偏微分多智能体系统的包容控制

摘要/Abstract

摘要：

该文研究一类偏微分多智能体系统的包容控制问题，该类系统是由二阶抛物型或二阶双曲型偏微分方程构建而成.基于网络拓扑结构，依据跟随者系统的输出形式，设计了P型迭代学习律，得到了系统基于迭代学习稳定性意义下的收敛性条件.利用压缩映射原理，证明了两类系统的包容误差在有限时间区间内随迭代次数的增加于L²空间中收敛到零.最后，仿真算例验证了理论分析的正确性.

关键词: 迭代学习算法, 偏微分方程, 多智能体系统, 包容控制

Abstract:

In this paper, we deals with the containment control problem for a class of partial differential multi-agent systems, which are composed of the second-order parabolic equations or the second-order hyperbolic equations. Based on the framework of network topologies, the P-type iterative learning law is designed depending on the output form of the follower system, and the convergence condition of the system in the sense of iterative learning stability is obtained. By using the contraction mapping method, it is proved that the containment errors of two kinds of systems on the finite time interval converge to zero on $L^2$ space with the increasing of iterations. Finally, simulation examples demonstrate the validity of the theoretical analysis.

Key words: Iterative learning algorithm, Partial differential equation, Multi-agent systems, Containment control

中图分类号:

TP13

张丹,傅勤,陈振杰. 基于迭代学习算法的偏微分多智能体系统的包容控制[J]. 数学物理学报, 2021, 41(4): 1111-1123.

Dan Zhang,Qin Fu,Zhenjie Chen. Containment Control for Partial Differential Multi-Agent Systems via Iterative Learning Algorithm[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1111-1123.

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