The paper deals with the optimization of nonlinear systems by using Extremum Seeking Control (ESC) without any prior knowledge of the system model. An Extend Kalman Filter based Extremum Seeking Control (EKF based ESC) is proposed, which can make the amplitude of perturbation signal variable and ensure convergence to zero, i.e. without steady-state oscillation. The proposed ESC algorithm makes also possible to obtain more accurate gradient estimate and more rapid ESC convergence. The proposed EKF based ESC algorithm is applied to a fifth-order model of anaerobic digestion process and its performances are compared with the performances of the classical ESC algorithm.

This paper proposes a Kalman filter (KF) based Newton extremum seeking control (NESC) to maximize production rates of hydrogen and methane in anaerobic digestion process. The Kalman filtering algorithm is used to obtain more accurate gradient and Hessian estimates which makes possible to increase the convergence speed to the extremum and to eliminate input and output steady-state oscillations. The simulation examples demonstrate the performances of the proposed approach.

In this paper, a new Newton-based extremum-seeking control for dynamic systems is proposed using Kalman filter for gradient and Hessian estimation as well as a stochastic perturbation signal with time-varying amplitude. The obtained Kalman filter based Newton extremum-seeking control (KFNESC) makes it possible to accelerate the convergence to the extremum and attenuate the steady-state oscillations. The convergence and oscillation attenuation properties of the closed-loop system with KFNESC are considered, and the proposed control is applied to a two-stages anaerobic digestion process in order to maximize the hydrogen production rate, which has better robustness and a slower steady-state oscillation with the comparison of Newton-based ESC and sliding mode ESC.