Two-Stage-Decoupled Approach for Distributed Prescribed-Time Resource Allocation on Unbalanced Digraphs

This paper investigates the prescribed-time distributed resource allocation problem over unbalanced directed graphs. A distributed, two-stage-decoupled algorithm is proposed. In the first stage, local out-degree information is employed to estimate the right eigenvector of the out-degree Laplacian matrix. In the second stage, a prescribed-time gradient-based optimization algorithm is developed based on the estimation result. The proposed method ensures that the global equality constraint is strictly satisfied during the entire process and guarantees the convergence of system states within a pre-assigned time. The decoupled structure enhances design flexibility and reduces implementation complexity. Numerical simulations are provided to validate the effectiveness of the proposed approach.