A Fixed-Time Convergent Distributed Algorithm for Time-Varying Optimal Resource Allocation Problem

This article proposes a distributed time-varying optimization approach to address the dynamic resource allocation problem, leveraging a sliding mode technique. The algorithm integrates a fixed-time sliding mode component to ensure that the global equality constraints are met, and is coupled with a fixed-time distributed control mechanism involving the nonsmooth consensus idea for attaining the system's optimal state. It is designed to operate with minimal communication overhead, requiring only a single variable exchange between neighboring agents. This algorithm can effectuate the optimal resource allocation in both scenarios with time-varying cost functions of identical and nonidentical Hessians, where the latter can be non-quadratic. The practicality and superiority of our algorithm are validated by case studies.