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Decentralized Formation Control with A Quadratic Lyapunov Function
In this paper, we investigate a decentralized formation control algorithm for
an undirected formation control model. Unlike other formation control problems
where only the shape of a configuration counts, we emphasize here also its
Euclidean embedding. By following this decentralized formation control law, the
agents will converge to certain equilibrium of the control system. In
particular, we show that there is a quadratic Lyapunov function associated with
the formation control system whose unique local (global) minimum point is the
target configuration. In view of the fact that there exist multiple equilibria
(in fact, a continuum of equilibria) of the formation control system, and hence
there are solutions of the system which converge to some equilibria other than
the target configuration, we apply simulated annealing, as a heuristic method,
to the formation control law to fix this problem. Simulation results show that
sample paths of the modified stochastic system approach the target
configuration
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