Analysis of multivariable extremum seeking algorithms

This paper presents a systematic approach for the analysis of extremum seeking algorithms (ESA). In applications, these algorithms are used to determine and track the parameters that optimize a system level cost function in real time. The design of multiparameter ESA is greatly facilitated by the availability of simple models that explain the algorithm operation. In this paper, a simple model for stability and performance calculations is given. The model approximates the behavior of the ESA with an accuracy that improves as the dither frequencies used by the ESA are increased. The model predicts ESA stability and performance even if the cost function measurements are corrupted by noise or additional process dynamics. The model is for the general case of multivariable online optimization. Our approach to the analysis supports the addition of dynamic compensation in the ESA. Guidelines for the selection of the dither and the dynamic compensator are derived from our model