Distributed Algorithm Design for Resource Allocation Problems of Second-Order Multiagent Systems Over Weight-Balanced Digraphs

This paper studies two distributed resource allocation problems of second-order systems over weight-balanced communication networks. In the first problem, the decisions of agents are coupled by network resource constraints, and in the second problem, the decisions of agents are constrained by local constraints and network resource constraints. Compared with many existing resource allocation problems, the formulation involves the dynamics of agents. The second-order dynamics of agents induce the difficult in algorithm design and analysis, since the decisions of agents could not be directly decided by their control inputs. In order to optimally allocate the network resource, two distributed algorithms are designed via state feedback and gradient descent for the two problems, respectively. Besides, the convergence of the two algorithms are analyzed. By the two algorithms, the second-order agents converge to the optimal allocation of the two problems, respectively. Finally, two examples about economic dispatch problems verify the two algorithms.