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Cone invariance and rendezvous of multiple agents 
Abstract 
In this article is presented a dynamical s … In this article is presented a dynamical systems framework for analysing multiagent rendezvous problems and characterize the dynamical behaviour of the collective system. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. The proposed approach is based on the set invariance theory and focusses on how to generate feedback between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions of the agents and the dynamics is modelled as linear firstorder systems. These algorithms have also been applied to nonlinear firstorder systems.
The rendezvous problem in the framework of cooperative and competitive dynamical systems is analysed that has had some remarkable applications to biological sciences. Cooperative and competitive dynamical systems are shown to generate monotone flows by the classical MullerKamke theorem, which is analysed using the set invariance theory. In this article, equivalence between the rendezvous problem and invariance of an appropriately defined cone is established. The problem of rendezvous is cast as a stabilization problem, with a the set of constraints on the trajectories of the agents defined on the phase plane. The nagent rendezvous problem is formulated as an ellipsoidal cone invariance problem in the ndimensional phase space. Theoretical results based on set invariance theory and monotone dynamical systems are developed. The necessary and sufficient conditions for rendezvous of linear systems are presented in the form of linear matrix inequalities. These conditions are also interpreted in the Lyapunov framework using multiple Lyapunov functions. Numerical examples that demonstrate application are also presented. emonstrate application are also presented. +


Authors  R Bhattacharya, A Tiwari, J Fung, R Murray + 
ID  2009s + 
Source  Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 223(6):779789 + 
Tag  bftm09jae + 
Title  Cone invariance and rendezvous of multiple agents + 
Type  Published version + 
Categories  Papers 
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15 May 2016 06:16:25 + 
URL This property is a special property in this wiki.

http://journals.pepublishing.com/index/y04282511wr7wl3v.pdf + 
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Cone invariance and rendezvous of multiple agents +  Title 
