Sufficient conditions for decentralized navigation functions based controllers using canonical vector fields

Author

Dimarogonas, Dimos V.

Author_Institution

ACCESS Linnaeus Center, R. Inst. of Technol., Stockholm, Sweden

fYear

2011

fDate

12-15 Dec. 2011

Firstpage

6433

Lastpage

6438

Abstract

A combination of dual Lyapunov analysis and properties of decentralized navigation function based controllers is used to check the stability properties of a certain class of decentralized controllers for navigation and collision avoidance in multi-agent systems. The derived results yield a less conservative condition from previous approaches, which relates to the negativity of the sum of the minimum eigenvalues of the Hessian matrices at the critical points, instead of requiring each of the eigenvalues to be negative itself. This provides an improved characterization of the reachable set of this class of decentralized navigation function based controllers, which is less conservative than the previous results for the same class of controllers.

Keywords

Hessian matrices; Lyapunov methods; collision avoidance; decentralised control; eigenvalues and eigenfunctions; multi-agent systems; multi-robot systems; set theory; stability; vectors; Hessian matrices; canonical vector fields; collision avoidance; decentralized navigation function based controllers; dual Lyapunov analysis; minimum eigenvalues; multiagent systems; reachable set; stability properties; Collision avoidance; Convergence; Density functional theory; Eigenvalues and eigenfunctions; Navigation; Trajectory; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Conference_Location

Orlando, FL

ISSN

0743-1546

Print_ISBN

978-1-61284-800-6

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2011.6161219

Filename

6161219