领导-跟随多智能体系统在自适应牵制控制下的部分分量一致性  

Partial component consensus of leader-following multi-agent systems via adaptive pinning control

作　　者：刘雪雪 李丰兵[1] 马忠军[1] LIU Xuexue;LI Fengbing;MA Zhongjun(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2021年第3期247-252,共6页Journal of Guilin University of Electronic Technology

基　　金：广西自然科学基金(2018GXNSFAA281068);桂林电子科技大学数学与计算科学学院院级研究生创新计划(2020YJSC-03)。

摘　　要：部分分量一致,是指随着时间的推移,多智能体系统中所有状态变量的某些分量渐近趋于恒同而其余分量不一定趋于恒同的一种现象。它是一种比恒同一致弱的群体动力学行为。为了减弱由领导者和跟随者构成的多智能体系统的不确定性所带来的影响,提出了一个自适应控制协议,探究了在适应性牵制控制协议下一阶多智能体系统的部分分量一致性问题。首先给出了部分分量一致的基础概念、定理及一些推论,利用置换矩阵方法将最初的偏差系统转化为新的偏差系统,使得多智能体系统的部分分量一致性问题转换为新的偏差系统中零解的部分变元稳定性问题。然后,构造Lyapunov函数并基于代数图论、矩阵理论及部分变元稳定性知识推出了一些充分性判据,从而确保多智能体系统按指数趋势实现部分分量一致。最后,运用数学软件MATLAB进行数值模拟,验证了理论推导结果的正确性及可行性。Partial component consensus refers to the phenomenon that some components of all state variables of multi-agent system tend to be identical asymptotically and the remaining components do not necessarily tend to be identical over time.It is a group dynamics behavior that is weaker than the general consensus.In order to reduce the influence of the uncertainty of the multi-agent system composed of leaders and followers,an adaptive control protocol is proposed to explore the partial component consensus of the first-order multi-agent system via adaptive pinning control.First,the basic concepts,theorems and some inferences of partial component consensus are given.The original error system is transformed into a new error system by means of permutation matrix.The partial component consensus problem of multi-agent system is transformed into the partial variable element stability problem of zero solution of new error system.Then,the Lyapunov function is constructed.With the help of algebraic graph theory,matrix theory and stability knowledge,it gets the sufficient criteria which guarantee the system to realize partial component consensus according to exponential trend.Finally,the MATLAB software is used for numerical simulation to illustrate the rationality of the conclusion.

关 键 词：多智能体系统 部分分量一致 自适应控制 牵制控制 领导者 

分 类 号：O231.2[理学—运筹学与控制论]