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

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>-<italic>logarithmic</italic> 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>-<italic>logarithmic</italic> 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.