Distributed Optimal Consensus Over Resource Allocation Network and Its Application to Dynamical Economic Dispatch

• Published in: IEEE transaction on neural networks and learning systems Vol. 29; no. 6; pp. 2407 - 2418
• Main Authors: Li, Chaojie, Yu, Xinghuo, Huang, Tingwen, He, Xing
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive systems; Computer simulation; Consensus; Continuous time systems; Convergence; distributed optimization; distributed primal–dual multiagent system; dynamical economic dispatch; Economics; Laplace equations; Linear programming; Multi-agent systems; Multiagent systems; Nonlinear programming; Optimization; Resource allocation; Resource management; Saddle points; Smart grid
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2017.2691760

The resource allocation problem is studied and reformulated by a distributed interior point method via a <inline-formula> <tex-math notation="LaTeX">\theta </tex-math></inline-formula>- logarithmic barrier. By the facilitation of the graph Laplacian, a fully distributed continuous-time multiagent system is developed for solving the problem. Specifically, to avoid high singularity of the <inline-formula> <tex-math notation="LaTeX">\theta </tex-math></inline-formula>- logarithmic barrier at boundary, an adaptive parameter switching strategy is introduced into this dynamical multiagent system. The convergence rate of the distributed algorithm is obtained. Moreover, a novel distributed primal-dual dynamical multiagent system is designed in a smart grid scenario to seek the saddle point of dynamical economic dispatch, which coincides with the optimal solution. The dual decomposition technique is applied to transform the optimization problem into easily solvable resource allocation subproblems with local inequality constraints. The good performance of the new dynamical systems is, respectively, verified by a numerical example and the IEEE six-bus test system-based simulations.