Observer design for a class of uncertain nonlinear systems with sampled outputs—Application to the estimation of kinetic rates in bioreactors

Abstract

A continuous–discrete time observer is proposed for a class of uncertain nonlinear systems where the output is available only at non uniformly spaced sampling instants. The underlying correction term depends on the output observation error and is updated in a mixed continuous-discrete fashion. The proposed observer is first introduced under a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. Two features of the proposed observer are worth to be pointed out. The first one consists in the simplicity of its calibration while the second one lies in its comprehensive convergence analysis. More specifically, it is shown that in the case of noise-free sampled outputs, the observation error lies in a ball centered at the origin and its radius is proportional to the bounds of the uncertainties and the sampling partition diameter. Moreover, in the free uncertainties case, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. The ability of the proposed observer to perform a suitable estimation of the reactions rates in biochemical reactors is highlighted through a simulation study dealing with an ethanolic fermentation.