Robust Constraint-Coupled Distributed Optimization With Nonuniform Communication Delay and Unknown Disturbances

Abstract

In this article, we address a constraint-coupled optimization problem over multiagent network systems with communication time delays and unknown disturbances. The primary objective is to minimize the sum of local cost functions while adhering to both local and global constraints, the latter encompassing subsets of all decision variables. The local costs are not required to be strictly or strongly convex, as long as they are convex. Utilizing a Lyapunov approach and linear matrix inequalities, a robust continuous-time algorithm is proposed to solve the problem under conditions of bounded variation rates and random communication time delays. The algorithm incorporates a disturbance rejection capability through a developed nonsingular fixed-time integral sliding mode strategy, thereby expanding its applicability. Illustrative examples are provided to demonstrate the effectiveness of the proposed approach.