Sliding Mode Multivariable Extremum Seeking Control with Application to Wind Farm Power Optimization

In this paper, a sliding mode based Extremum Seeking (ES) control scheme is proposed to solve a class of multivariable optimization problems. This approach recasts the problem of multivariable ES control into a sequence of single variable ES control. Our approach is suitable for non-separable problems, differentiating itself from previous work in this area. We determine the stability and convergence conditions from the unidimensional case and derive a sufficient condition for the multivariable scheme to converge to the vicinity of the optimal points. We investigate the application of the proposed scheme to optimize energy production in wind farms. Simulations are provided to illustrate the theoretical results and demonstrate its potential use.

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