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Nonlinear adaptive stabilizing control of an anaerobic digestion model with unknown kinetics

In this paper, we consider a nonlinear model of a biological wastewater treatment process, on the basis of two microbial populations and two substrates. The model, described by a four‐dimensional dynamic system, is known to be practically validated and reliable. We propose a feedback control law for asymptotic stabilization of the closed‐loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is applied to stabilize the dynamics towards an equilibrium point with maximal methane flow rate. Computer simulations are reported to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.