A distributed extremum seeking scheme for networked optimization

In this paper, a distributed extremum seeking scheme is proposed to find the solution of a non-model-based distributed optimization problem among networked agents. The agents are supposed to have measurements of the local cost functions and constraints. However, no explicit expressions on the cost functions, the constraints 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 semi-globally practically asymptotically (SPA) stable under the proposed extremum seeking law.