Nonlinear extremum seeking inspired on second order sliding modes

We present a new Extremum Seeking algorithm that uses Super-Twisting like nonlinear terms in order to improve its precision. In addition, the algorithm is combined with Second Order Sliding Mode observers to build an optimization framework for uncertain dynamic systems in which the variable to optimize is not measured and needs to be estimated. The relevance of the proposed framework is illustrated in the problem of biomass optimization of a biological reactor with uncertain kinetics.