Predefined-time optimization for distributed resource allocation

Abstract To meet certain quality and safety standards, convergence in predefined time to the optimal solution of optimization problems is always sought in many applications. In this paper, a novel distributed predefined-time convergent algorithm is proposed for the resource allocation problem. A distributed parameter learning method is introduced, which guarantees the fully distributed characterization of the proposed algorithm. Specifically, by employing nonhomogeneous functions with exponential terms, the proposed algorithm can achieve a predefined-time convergence rate, which further allows the convergence time to be a user-defined parameter. The proposed algorithm is faster than the asymptotically convergent and exponentially convergent algorithms and current fixed-time convergent algorithms. Moreover, with the convergence time of the proposed algorithm being an implicit parameter of the system, it can achieve convergence in any predefined time with properly-chosen system parameters, which contributes to the fast convergence of the proposed algorithm. Application to the power dispatch problem verifies the result, which demonstrates that the convergence rate of the proposed algorithm far outweighs that of current fixed-time convergent algorithms.