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'American Institute of Mathematical Sciences (AIMS)'
Doi
Abstract
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 edgetension
distance functions and triangular-area functions, and illustrate their
applications in the context of distributed coordination and formation control.This work was supported by the Australian Research Council
under grant DP160104500, and by JSPS KAKENHI Grant number JP17H03281
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