Distributed optimization in predefined-time for multi-agent systems over a directed network

Abstract

This paper is concerned with the distributed optimization problem (DOP) with equality constraints in predefined time for multi-agent systems (MASs) over a directed network. Firstly, a new principle with respect to the predefined-time convergence is developed for absolute continuous functions, which plays a key role in the consensus analysis later. Secondly, a novel control protocol is designed to address the solution of the considered DOP with convex objective functions. Thirdly, on the basis of Lyapunov functional approach and the proposed convergence principle, the predefined-time consensus conditions are achieved. Under the designed control protocol, the consensus state can reach feasible region in finite time, and subsequently converges to an optimal solution. Finally, the correctness of the theoretical analysis and the feasibility of the designed control strategy are verified by two illustrative simulations and an application example.