Prescribed-time distributed resource allocation algorithm for heterogeneous linear multi-agent networks with unbalanced directed communication

In this paper, a prescribed-time distributed algorithm is proposed to solve the resource allocation problem among the heterogeneous linear multi-agent systems over unbalanced directed networks. First, an estimator with prescribed-time convergence performance is designed to cope with the asymmetry of the unbalanced network topology. Then, a novel prescribed-time convergence result that features an adjustable convergence rate is developed. Based on this result, it is shown that the algorithm developed in this paper ensures the agents' outputs accurately reach the optimal solution within a prescribed-time and they are maintained at the optimum thereafter. Furthermore, a parameter selection rule is formulated to reflect the low conservatism of the algorithm. This indicates that the parameters affecting the convergence speed of the algorithm are not necessary to rely on the global information. Finally, the performance of the proposed algorithm is illustrated through simulations.