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Robust impulsive observer design for infinite‐dimensional cell population balance models
Author(s) -
Schaum Alexander,
Jerono Pascal,
Feketa Petro
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5852
Subject(s) - control theory (sociology) , mathematics , observer (physics) , convergence (economics) , kalman filter , numerical stability , stability (learning theory) , population , ordinary differential equation , exponential stability , differential equation , numerical analysis , mathematical analysis , computer science , nonlinear system , statistics , physics , demography , control (management) , quantum mechanics , artificial intelligence , machine learning , sociology , economics , economic growth
The 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‐spaceL 1 × ℝ +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.