Asynchronous distributed optimization with minimal communication

We consider problems where multiple agents must 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, especially when the agents are wireless devices with limited energy, we seek conditions under which communication of state information among nodes is asynchronous and can be minimized while still ensuring that the optimization process converges. We propose a scheme that limits communication to instants when some state estimation error function at a node exceeds a threshold and prove that, under certain conditions, such convergence is guaranteed. We apply this approach to a sensor network coverage control problem where the objective is to maximize the probability of detecting events occurring in a given region.