Adaptive observers for nonlinearly parameterized class of nonlinear systems

In this paper, one proposes adaptive observers for a class of uniformly observable MIMO nonlinear 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.