A Distributed Dynamical System for Optimal Resource Allocation Over State-Dependent Networks

Abstract

This paper focuses on investigating the nonsmooth resource allocation problem based on distributed dynamical systems over state-dependent communication networks. Taking into account the coupling of supply-demand constraint, a potential-based Lagrangian function containing local multipliers is reformulated by the exact penalty method. By virtue of the primal-dual subgradient flow, a distributed differentiated projected dynamical system with a state-dependent gain is proposed. It is shown that the connectivity of communication networks can be preserved under the proposed system. Furthermore, it is proved that the system converges to the optimal resource allocation with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/t)$</tex-math></inline-formula> convergence rate. Finally, the theoretical results are substantiated through simulations of economic dispatch problems in the IEEE 30-bus system and IEEE 118-bus system.