Adaptive observers for nonlinearly parametrized class of nonlinear systems

Mondher Farza (1) , Mohammed M'Saad (1) , Tarek Maatoug (1) , Mohammed Kamoun (2)

1 Equipe Automatique - Laboratoire GREYC - UMR6072
2 CEM Lab - ENIS - Département de Génie Électrique de Sfax [ENIS]

In this paper, one proposes adaptive observers for a class of uniformly observableMIMOnonlinear systems with general nonlinear parameterizations. The state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well-defined persistent excitation condition. Moreover, the gain of the observers involves a design function that has to satisfy a simple condition which is given. Different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. The theory is supported by simulation results related to the estimation of the biomass concentration and the Contois model parameters in a bioreactor.

Mots clés: Nonlinear system; Nonlinear parameterization; Adaptive observer; Persistent excitation; High gain observer; Sliding mode observer

Domaines: Automatique; Automatique / Robotique

Mondher Farza, Mohammed M'Saad, Tarek Maatoug, Mohammed Kamoun. Adaptive observers for nonlinearly parametrized class of nonlinear systems. Automatica, 2009, 45 (10), pp.2292-2299. ⟨10.1016/j.automatica.2009.06.008⟩. ⟨hal-01058820⟩