Robust impulsive observer design for infinite‐dimensional cell population balance models

Abstract

AbstractThe observer design problem for a class of cell population balance models, describing the time evolution of the cell mass density distribution function and the substrate concentration in a continuous‐stirred tank bioreactor with irregular discrete‐time measurements of the cell mass distribution is considered. The model consists of a partial integro‐differential equation coupled with an ordinary differential equation. Using the theory of impulsive systems sufficient conditions for the input‐to‐state‐stability (ISS) of the observation error in the state‐space with respect to the measurement uncertainty are derived in terms of the maximum time between successive measurements and the ISS gain. In absence of measurement uncertainty the convergence conditions imply exponential stability of the observation error dynamics. Besides these rigorous conditions, application‐oriented tuning guidelines are established. The theoretical results are illustrated with numerical simulations including a comparison with a continuous–discrete extended Kalman filter based on the numerical approximation, showing that a similar accuracy is achieved when using a finite‐dimensional approximation of the proposed impulsive observer scheme with a considerably lower computational effort.