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Distributed Feedback Optimisation for Robotic Coordination

Feedback optimisation is an emerging technique aiming at steering a system to an optimal steady state for a given objective function. We show that it is possible to employ this control strategy in a distributed manner. Moreover, we prove asymptotic convergence to the set of optimal configurations. To this scope, we show that exponential stability is needed only for the portion of the state that affects the objective function. This is showcased by driving a swarm of agents towards a target location while maintaining a target formation. Finally, we provide a sufficient condition on the topological structure of the specified formation to guarantee convergence of the swarm in formation around the target location.