Discrete-Time Extremum Seeking Control Applied to a Fermentation Process

In this paper, a very simple discrete-time extremum-seeking control strategy is proposed from the classical direct search gradient-based optimization algorithm. First, the optimization problem to solve and solvability conditions are presented. Then, the discrete-time extremum-seeking strategy is developed and its convergence is assured by demonstrating that the optimization error dynamics is globally asymptotically stable. Finally, the feasibility of the proposed extremum-seeking algorithm is demonstrated by simulations on a fermentation reactor for bioethanol production.