Asynchronous distributed optimization with minimal communication and connectivity preservation

We consider problems where multiple agents cooperate to control their individual state so as to optimize a common objective while communicating with each other to exchange state information. Since communication costs can be significant, we seek conditions under which communication of state information among nodes can be minimized while still ensuring that the optimization process converges. In prior work, an asynchronous (event-driven) optimization scheme was proposed that limits communication to instants when some state estimation error function at a node exceeds a threshold. It was shown that convergence is guaranteed under no communication delays. In this paper, we first prove that convergence is still guaranteed under bounded communication delays. Next, we propose a decentralized mechanism which provably preserves network connectivity by using each node´s routing information. We apply the optimization scheme to a sensor network coverage control problem where the objective is to maximize the probability of detecting events occurring in a region and show that the proposed asynchronous approach significantly reduces communication costs, hence also prolonging the system´s lifetime, without any performance degradation.