Distributed resource allocation via multi-agent systems under time-varying networks

Abstract

In this paper, the problem of distributed resource allocation with coupled equality, nonlinear inequality and convex set constraints is studied. Each agent only has access to the information associated with its own cost function, inequality constraints, convex set constraint, and a local block of the coupled equality constraints. To address such problem, a new distributed primal–dual algorithm is proposed for a continuous-time multi-agent system under a time-varying graph. In the proposed algorithm, two consensus strategies are employed. One is used to estimate the coupled equality constraint function, and the other one is used to estimate corresponding optimal dual variable. Furthermore, a novel Lyapunov function is constructed based on a strongly convex function to analyze convergence of the algorithm. The results show that if the time-varying graph is balanced and the union in a certain period is strongly connected, the algorithm asymptotically converges, and the convergence state is the solution to the distributed resource allocation problem. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.