Distributed Optimization for Graph Matching.

Graph matching, or the determination of the vertex correspondences between a pair of graphs, is a crucial task in various problems in different science and engineering disciplines. This article aims to propose a distributed optimization approach for graph matching (GM) between two isomorphic graphs over multiagent networks. For this, we first show that for a class of asymmetric graphs, GM of two isomorphic graphs is equivalent to a convex relaxation where the set of permutation matrices is replaced by the set of pseudostochastic matrices. Then, we formulate GM as a distributed convex optimization problem with equality constraints and a set constraint, over a network of multiple agents. For arbitrary labelings of the vertices, each agent only has information about just one vertex and its neighborhood, and can exchange information with its neighbors. A projected primal-dual gradient method is developed to solve the constrained optimization problem, and globally exponential convergence of the agents' states to the optimal permutation is achieved. Finally, we illustrate the effectiveness of the algorithm through simulation examples.

Distributed Coordination for Optimal Energy Generation and Distribution in Cyber-Physical Energy Networks.

This paper proposes three coordination laws for optimal energy generation and distribution in energy network, which is composed of physical flow layer and cyber communication layer. The physical energy flows through the physical layer; but all the energies are coordinated to generate and flow by distributed coordination algorithms on the basis of communication information. First, distributed energy generation and energy distribution laws are proposed in a decoupled manner without considering the interactive characteristics between the energy generation and energy distribution. Second, a joint coordination law to treat the energy generation and energy distribution in a coupled manner taking account of the interactive characteristics is designed. Third, to handle over- or less-energy generation cases, an energy distribution law for networks with batteries is designed. The coordination laws proposed in this paper are fully distributed in the sense that they are decided optimally only using relative information among neighboring nodes. Through numerical simulations, the validity of the proposed distributed coordination laws is illustrated.