具有执行器饱和的多智能体系统$H_\infty$边界一致性控制

doi:10.12341/jssms22224

系统科学与数学 ›› 2023, Vol. 43 ›› Issue (1): 29-43.DOI: 10.12341/jssms22224

具有执行器饱和的多智能体系统$H_\infty$边界一致性控制

钟佳岐¹, 陈晓雷¹, 曾诚²

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

收稿日期:2022-04-01 修回日期:2022-08-03 出版日期:2023-01-25 发布日期:2023-02-24
基金资助:
国家自然科学基金（62003066，62163008），重庆市自然科学基金（cstc2021jcyj-msxmX0331），重庆市教委科学技术研究项目（KJQN201900614）资助课题.

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钟佳岐, 陈晓雷, 曾诚. 具有执行器饱和的多智能体系统$H_\infty$边界一致性控制[J]. 系统科学与数学, 2023, 43(1): 29-43.

ZHONG Jiaqi, CHEN Xiaolei, ZENG Cheng. $H_\infty$ Boundary Consensus Control for Multi-Agent Systems with Actuator Saturation[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(1): 29-43.

$H_\infty$ Boundary Consensus Control for Multi-Agent Systems with Actuator Saturation

ZHONG Jiaqi¹, CHEN Xiaolei¹, ZENG Cheng²

1. College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065;
2. College of Science, Guizhou Institute of Technology, Guiyang 550003

Received:2022-04-01 Revised:2022-08-03 Online:2023-01-25 Published:2023-02-24

为了解决具有时空耦合特性的多智能体系统在执行器饱和约束下的一致性跟踪问题，文章提出了一种受限$H_\infty$边界控制策略.首先针对领导者与跟随者的时空动力学行为特征，运用克罗内克积与等价有向图，将跟踪问题转化为镇定问题，构建出由多个抛物线型偏微分方程（partial differential equation，PDE）组成的一致性误差系统.其次，通过改进李雅普诺夫方法和沃廷格不等式，推导出同时满足$H_\infty$增益和指数稳定的充分条件.再次，融合不变集理论，在线性矩阵不等式（linear matrix inequality，LMI）多目标优化的框架下，解决了Neumann边界控制器的饱和问题.最后，通过对比仿真验证了所提出方法的有效性.

关键词： 多智能体, 一致性, 边界控制, 执行器饱和, $H_\infty$控制

In order to solve the tracking problem of multi-agent systems with spatiotemporal coupling characteristics under the actuators saturation, this paper proposes a constrained $H_\infty$ boundary consensus control strategy. First, by applying the Kronecker product and equivalent directed graph, the original consensus tracking problem is transformed into the stabilization problem of multi-agent error systems, whose model involves the multiple parabolic partial differential equations (PDEs) with Neumann boundary conditions. Subsequently, a sufficient condition on the $H_\infty$ norm and exponential stability is obtained by improving the Lyapunov-based method and Wirtinger's inequality. Then, the actuator saturation problem of Neumann boundary control is addressed by using the invariant set theory in the multi-objective optimization framework of linear matrix inequality (LMI). Finally, the comparison simulation results demonstrate the effectiveness of proposed methodology.

Key words: Multi-agent system, consensus, boundary control, actuator saturation, $H_\infty$ control

MR(2010)主题分类:

35Q93
93B36

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