Distributed Time-Varying Optimization Over a Strongly Connected and Weight-Balanced Digraph

This paper deals with the distributed time-varying optimization problem over a digragh (or directed graph). Motivated by the time-varying nature present in the cost functions, we model the time-varying features using an exosystem and formulate the problem of minimizing a global cost function, which is the sum of the local time-varying cost functions. We design a distributed algorithm for each agent that only utilizes the information of its own cost function and the information obtained through a network represented by a strongly connected and weight-balanced digraph. Convergence analysis is carried out to show that the decision variables of all agents converge to the time-varying optimal solution with time. Simulation results verify the theoretical conclusions.