Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems
Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems
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DOI：
10.3934/naco.2019020
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Zhiyong Sun;T. Sugie
中科院分区：
文献类型：
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作者：
Zhiyong Sun;T. Sugie
多智能体协调控制通常包含对全局控制任务信息进行编码的势函数，而单个智能体的控制输入通常采用基于梯度的控制律来设计。在基于梯度的协调控制系统的平衡点稳定性分析中，与势函数相关的Hessian矩阵的性质起着重要的作用。因此，基于梯度的多智能体协调系统中Hessian矩阵的辨识成为多智能体均衡分析的关键步骤。然而，通常通过入口计算来识别Hessian矩阵是一项非常繁琐的任务，并且很容易引入计算误差。本文提出了几种基于矩阵微分和微积分规则的Hessian矩阵的一般快速辨识方法，可以很容易地推导出多智能体协调系统的Hessian矩阵的紧凑形式。本文还介绍了几种典型势函数（包括边缘张力距离函数和三角面积函数）的Hessian识别实例，并举例说明了它们在分布式协调和群体控制中的应用。
Multi-agent coordination control usually involves a potential function that encodes information of a global control task, while the control input for individual agents is often designed by a gradient-based control law. The property of Hessian matrix associated with a potential function plays an important role in the stability analysis of equilibrium points in gradient-based coordination control systems. Therefore, the identification of Hessian matrix in gradient-based multi-agent coordination systems becomes a key step in multi-agent equilibrium analysis. However, very often the identification of Hessian matrix via the entry-wise calculation is a very tedious task and can easily introduce calculation errors. In this paper we present some general and fast approaches for the identification of Hessian matrix based on matrix differentials and calculus rules, which can easily derive a compact form of Hessian matrix for multi-agent coordination systems. We also present several examples on Hessian identification for certain typical potential functions involving edge-tension distance functions and triangular-area functions, and illustrate their applications in the context of distributed coordination and formation control.