Predefined-Time Distributed Optimal Allocation of Resources: A Time-Base Generator Scheme

In this article, we present a novel predefined-time distributed optimization protocol for the resource allocation problem (RAP). Different from the existing finite/fixed-time distributed optimal algorithms, the proposed protocol is built on the time-varying time-based-generator scheme. The settling time is independent of the initial values of the agents and any designed parameters, which implies that the settling time can be predesigned by the user. To address the inequality constraints, the
$\epsilon $
-exact penalty function method is introduced to solve the RAP within a predefined-time. In addition, the designed optimization protocol can be implemented in an initialization-free manner, which makes the algorithms feasible under arbitrary initial states. Finally, several numerical simulation results are provided to demonstrate the effectiveness of the proposed algorithms.