Solving specified-time distributed optimization problem via sampled-data-based algorithm

TL;DR

This paper introduces a novel sampled-data-based distributed optimization algorithm that guarantees convergence to the optimal solution within a pre-specified time, independent of initial conditions and network topology.

Contribution

It presents the first specified-time distributed optimization algorithm for directed networks that operates with discrete sampling and maintains constraints throughout.

Findings

Exact predefined settling time achieved

Reduced communication via discrete sampling

Always satisfies equality constraints during optimization

Abstract

Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time. Herein, we design a specified-time distributed optimization algorithm for connected agents with directed topologies to collectively minimize the sum of individual objective functions subject to an equality constraint. With the designed algorithm, the settling time of distributed optimization can be exactly predefined. The specified selection of such a settling time is independent of not only the initial conditions of agents, but also the algorithm parameters and the communication topologies. Furthermore, the proposed algorithm can realize specified-time optimization by exchanging information among neighbours only at discrete sampling instants and thus reduces the communication burden. In addition, the equality constraint is always satisfied during the whole process, which makes the proposed algorithm applicable to online solving distributed optimization problems such as economic dispatch. For the special case of undirected communication topologies, a reduced-order algorithm is also designed. Finally, the effectiveness of the theoretical analysis is justified by numerical simulations.