An application of Rantzer's Dual Lyapunov Theorem to decentralized navigation

Dimos V. Dimarogonas, Kostas J. Kyriakopoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We provide a connection between Rantzer's dual Lyapunov Theorem that appeared in [18] with Decentralized Navigation Functions (DNFs). It is shown that when the agents' control law does not contain an element that forces them to cooperate with the rest of the team once they have reached their desired goal, global convergence cannot be guaranteed. A sufficient condition for this to happen is derived based on Rantzer's Theorem. In particular, it is shown that agents are driven towards their goals provided that collisions between the team members tend to occur whenever agents are found sufficiently far from their desired destinations. This is derived based on the properties of the critical points of the DNF's imposed by Rantzer's Theorem. The result can be used as a new approach to guaranteed local-minima free decentralized control approaches.

Original languageEnglish (US)
Title of host publication2007 Mediterranean Conference on Control and Automation, MED
DOIs
StatePublished - 2007
Event2007 Mediterranean Conference on Control and Automation, MED - Athens, Greece
Duration: Jul 27 2007Jul 29 2007

Publication series

Name2007 Mediterranean Conference on Control and Automation, MED

Other

Other2007 Mediterranean Conference on Control and Automation, MED
Country/TerritoryGreece
CityAthens
Period7/27/077/29/07

ASJC Scopus subject areas

  • Artificial Intelligence
  • Control and Systems Engineering

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