Distributed continuous-time algorithm for resource allocation over unbalanced directed networks

The problem we aim to solve in this study is the distributed resource allocation problem (DRAP) over unbalanced directed networks, in which the local inequality constraint and global equality constraint are considered. On the basis of the fixed-time projection method, a distributed gradient algorithm is developed. The corresponding eigenvalue is obtained within fixed-time by tapping the row-stochastic or column-stochastic Laplacian matrix to overcome the unbalance of directed weights. Therefore, the optimal solution can be obtained asymptotically. Moreover, the proposed algorithm is initialization-free and its control parameters are constant. Finally, the effectiveness is illustrated by several case studies. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Automated summary

This study addresses the distributed resource allocation problem over unbalanced directed networks with local inequality constraint and global equality constraint. A distributed gradient algorithm is developed based on the fixed-time projection method, and the corresponding eigenvalue is obtained within fixed-time by tapping the row-stochastic or column-stochastic Laplacian matrix to overcome the unbalance of directed weights. Therefore, the optimal solution can be obtained asymptotically. The proposed algorithm is initialization-free and has constant control parameters. The effectiveness is demonstrated through several case studies.