Cooperative Extremum Seeking Control via Sliding Mode for Distributed Optimization

Abstract

In this paper, a cooperative distributed optimization method via sliding mode extremum seeking (ES) control for a class of large-scale interconnected systems is presented. In this approach, a consensus algorithm is exploited to communicate the value of the global cost function to the ES controllers. Then, each sliding mode ES controller is designed such that a multivariable cost function is optimized in a cooperative fashion. The stability and convergence conditions for the ES controllers are determined and sufficient conditions for the distributed scheme to converge to the vicinity of the optimal points are driven. The application of the proposed scheme to a real-world example is investigated and simulations are provided to illustrate the theoretical results and demonstrate their potential use.