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Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems

Sun, Zhiyong LU and Sugie, Toshiharu (2019) In Numerical Algebra, Control and Optimization 9(3). p.297-318
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... (More)
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. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Multi-agent coordination, Hessian matrix, gradient-based control
in
Numerical Algebra, Control and Optimization
volume
9
issue
3
pages
297 - 318
publisher
AIMS Press
external identifiers
  • scopus:85079058862
ISSN
2155-3297
DOI
10.3934/naco.2019020
language
English
LU publication?
yes
id
a744cd95-ba0c-460e-93ad-d311f1c8a978
date added to LUP
2018-10-12 16:02:30
date last changed
2020-04-07 10:25:53
@article{a744cd95-ba0c-460e-93ad-d311f1c8a978,
  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 edge-tension distance functions and triangular-area functions, and  illustrate their applications   in the context of distributed coordination and formation control.},
  author       = {Sun, Zhiyong and Sugie, Toshiharu},
  issn         = {2155-3297},
  language     = {eng},
  number       = {3},
  pages        = {297--318},
  publisher    = {AIMS Press},
  series       = {Numerical Algebra, Control and Optimization},
  title        = {Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems},
  url          = {https://lup.lub.lu.se/search/ws/files/52919592/NACO_201810_Hessian_calculation_final.pdf},
  doi          = {10.3934/naco.2019020},
  volume       = {9},
  year         = {2019},
}