-The objective of this study is to improve the performance of the extremum-seeking control ( ) technique in terms of time and accuracy of convergence towards the optimum operating point of a dynamic system subject to the effect of external disturbances. More precisely, the idea is to reduce the undesirable effect of time scale separation in on the performance of the closed loop system. The method consists in adaptively controlling the excitation signal amplitude using a neural network (NN) model, which gives a real-time estimate of the optimal operating point based on the measurement of the external disturbances. Stability of the proposed with adaptive excitation, referred to in the following as , is demonstrated. The superiority of compared to in terms of accuracy and time of convergence to the optimum is demonstrated both theoretically and experimentally, in the case of the optimization of a photovoltaic panel system (PV).

During the last decade, the microbial fuel cell (MFC) has been considered as a promising solution to produce renewable energy while reducing the excessive consumption of electrical energy in wastewater treatment centers. One of the problems facing the use of an MFC as a battery is the fact that its internal resistance varies with various external sources of disturbances causing a variation in its optimal point of operation. In this case the use of a real-time optimization method is necessary for the battery to work at its optimum. Extremum seeking control (ESC) can be applied to optimize the system. However, in the case where important external disturbances cause rapid changes in the optimal operating point, ESC converges to a point other than the desired optimum because of its very slow convergence rate. In this paper, a method which judiciously combines an ESC routine with a neural-network based anticipatory action is proposed. The anticipatory action takes into account a measurable external disturbance, namely the inlet substrate concentration. Simulation results show that the proposed scheme leads to an improvement of the convergence rate towards the desired optimum.

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