Cascade predictors design for a class of nonlinear uncertain systems with delayed state — Application to bioreactor
Résumé
The present work proposes a cascade predictor for a class of uncertain nonlinear systems in the presence of uncertainties in the state equations. The delayed state is assumed to be available with an arbitrarily long delay and the underlying measurements are assumed to be corrupted by an additive bounded unknown function. The proposed predictor is constituted by a cascade of subsystems where each of these subsystems predicts the state of the preceding one with a prediction horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The design of the predictor is achieved by assuming a set of conditions under which the ultimate boundedness of the estimation error is established. It was in particular shown that in the absence of uncertainties, the observation error converges exponentially to zero. In the presence of uncertainties, the asymptotic observation error remains in a ball which radius depends in particular on the magnitudes of the delay, the Lipschitz constant of the systems nonlinearities and the bounds of the considered uncertainties. The performance of the proposed observer and its main properties are highlighted through an typical example dealing with a bioreactor.