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Finite time distributed distance‐constrained shape stabilization and flocking control for d ‐dimensional undirected rigid formations
Author(s) -
Sun Zhiyong,
Mou Shaoshuai,
Deghat Mohammad,
Anderson Brian D. O.
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3477
Subject(s) - control theory (sociology) , settling time , convergence (economics) , flocking (texture) , exponential stability , rigid body , integrator , computer science , mathematics , control (management) , control engineering , engineering , physics , bandwidth (computing) , nonlinear system , computer network , classical mechanics , quantum mechanics , artificial intelligence , economics , step response , economic growth
Summary Most of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.