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

Dimarogonas, DV; Kyriakopoulos, KJ

dc.contributor.author	Dimarogonas, DV	en
dc.contributor.author	Kyriakopoulos, KJ	en
dc.date.accessioned	2014-03-01T02:44:25Z
dc.date.available	2014-03-01T02:44:25Z
dc.date.issued	2007	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31822
dc.subject	Critical Point	en
dc.subject	Decentralized Control	en
dc.subject	Global Convergence	en
dc.subject	Local Minima	en
dc.subject.other	Equations of state	en
dc.subject.other	Industrial engineering	en
dc.subject.other	Navigation	en
dc.subject.other	Control and automation	en
dc.subject.other	Control approaches	en
dc.subject.other	Control laws	en
dc.subject.other	Critical points	en
dc.subject.other	Decentralized navigation	en
dc.subject.other	Global convergence	en
dc.subject.other	LYAPUNOV theorems	en
dc.subject.other	New approaches	en
dc.subject.other	Sufficient conditions	en
dc.subject.other	Team members	en
dc.subject.other	Telecommunication networks	en
dc.title	An application of Rantzer's Dual Lyapunov Theorem to decentralized navigation	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/MED.2007.4433911	en
heal.identifier.secondary	4433911	en
heal.identifier.secondary	http://dx.doi.org/10.1109/MED.2007.4433911	en
heal.publicationDate	2007	en
heal.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. ©2007 IEEE.	en
heal.journalName	2007 Mediterranean Conference on Control and Automation, MED	en
dc.identifier.doi	10.1109/MED.2007.4433911	en