Distributed Extremum Seeking for Optimal Resource Allocation and Its Application to Economic Dispatch in Smart Grids.

Abstract

This paper proposes a first-order extremum-seeking algorithm to solve the resource allocation problem, where the specific expression form and gradient information of the local cost functions are not required. Agents take advantage of measurements of local cost functions to minimize the sum of their cost functions while satisfying the resource constraint, where agents exchange the estimated decisions with their neighbors under an undirected and connected graph. Making use of the Lyapunov stability theory and the average analysis method, the convergence of the proposed algorithm to the neighborhood of the optimal solution is presented. In addition, it is obtained that the designed algorithm is semiglobally practically asymptotically stable. Then, the first-order algorithm is extended to the second-order algorithm with low-pass filters, which achieves better convergence performance than the first-order algorithm. Finally, the effectiveness of the proposed algorithm is illustrated by numerical examples and its application to economic dispatch in smart grids.