A Specified-Time Distributed Optimization Algorithm for Multi-Agent Systems With Time-Varying Constraints

In this paper, a class of distributed optimization problems for multi-agent systems subject to time-varying coupling equality constraint is investigated. The global objective function is a sum of local convex objective functions and only local information is exchanged among the agents over a connected and undirected communication network. Based on convex optimization and Lyapunov stability theory, we show that the multi-agent system in closed loop with the proposed distributed protocol is able to converge to the time-dependent unique optimum within a specified time. Remarkably, the convergence time is independent of the initial conditions and can be specified in advance making the proposed scheme suitable for application with strict requirements on the convergence. We validate through simulations the effectiveness of the theoretical results.