Distributed Extremum Seeking for Constrained Networked Optimization and Its Application to Energy Consumption Control in Smart Grid

In this paper, a distributed extremum seeking scheme is proposed to find the solution of a nonmodel-based distributed optimization problem among networked agents. The agents are supposed to have measurements of the local cost functions and constraint functions. However, no explicit expressions on the cost functions, the constraint functions, or their gradients are available. The design of the distributed extremum seeking scheme is based on the saddle point dynamics. Stability analysis is conducted via using averaging analysis, Lyapunov stability analysis, and the concept of saddle point. It is shown that the solution to the distributed optimization problem is semiglobally practically asymptotically stable under the proposed extremum seeking law. An application of the proposed extremum seeking method to energy consumption control for the electricity consumers in smart grid is discussed. Simulation results on energy consumption control of a network of heating ventilation and air conditioning systems are provided to validate the proposed distributed extremum seeker.