Adaptive Estimation in Nonlinearly Parameterized Discrete-Time Nonlinear Systems

This paper proposes an uncertainty set update method for a class of discretetime nonlinearly parameterized systems. The method is based on the sequential application of a method proposed for linearly parameterized uncertain nonlinear systems in which the nonlinearly parameterized systems can be treated as linearly parameterized uncertain systems at each step. It is demonstrated that, given a persistence of excitation condition, convergence of the parameter estimates is guaranteed. The application of this method is applied to highly nonlinear system of a bioreactor operating under Monod kinetics.