Distributed algorithm design for constrained resource allocation problems with high-order multi-agent systems

Abstract

This paper studies distributed resource allocation problems of multi-agent systems, where the decisions of agents are subject to inequality network resource constraints and local inequality constraints. Compared with well-known resource allocation problems, our problem considers the high-order dynamics of agents. Without involving the control of high-order dynamics, existing distributed resource allocation algorithms cannot deal with our problem. Meanwhile, the high-order dynamics together with the inequality constraints makes it difficult to design and analyze distributed resource allocation algorithms, because the outputs of agents cannot be decided by their inputs directly and the optimal decisions of agents must satisfy the inequality constraints. In order to control the high-order agents to accomplish the resource allocation tasks autonomously, a distributed algorithm is designed by state feedback, gradient descent and primal–dual methods. Moreover, the convergence of the algorithm is analyzed by convex analysis and Lyapunov stability theory. With the algorithm, the high-order agents converge to the optimal allocation. Finally, numerical simulations verify the effectiveness of the algorithm.