Distributed convex optimization of discrete-time multi-agent systems: a new model

Consider a multi-agent system in which the states of the agents evolve in discrete time. Each agent is assigned a local convex cost function and the agents collectively wish to minimize the sum of all the cost functions. Under the assumption that the agent dynamics are first order and the agents communicate according to a strongly connected and weight-balanced digraph, we present a distributed algorithm to minimize the cost function. This algorithm is a discrete-time counterpart of similar algorithms that have been proposed in the literature for continuous time systems. We show that the algorithm converges exponentially to the optimal solution. We further extend the algorithm to consider an event triggered implementation that reduces the communication among the agents at the cost of a lower convergence rate.