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This paper studies a distributed continuous-time aggregative optimizationproblem, which is a fundamental problem in the price-based energy management.The objective of the distributed aggregative optimization is to minimize thesum of local objective functions, which have a specific expression that relieson agents' own decisions and the aggregation of all agents' decisions. To solvethe problem, a novel distributed continuous-time algorithm is proposed bycombining gradient dynamics with a dynamic average consensus estimator in atwo-time scale. The exponential convergence of the proposed algorithm isestablished under the assumption of a convex global cost function by virtue ofthe stability theory of singular perturbation systems. Motivated by practicalapplications, the implementation of the continuous-time algorithm withevent-triggered communication is investigated. Simulations on the price-basedenergy management of distributed energy resources are given to illustrate theproposed method.

Distributed event-triggered aggregative optimization with applications to price-based energy management