Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems

This study deals with constant-gain adaptive observers for nonlinear systems, for which relatively few solutions are available for some particular cases. We introduce an asymptotic observer of constant gain for nonlinear systems that have linear input. This allows the observer design to be formulate...

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Bibliographic Details
Published in:	Frontiers of information technology & electronic engineering Vol. 22; no. 1; pp. 68 - 78
Main Authors:	Torres, Jorge A., Sonck, Arno, Čelikovský, Sergej, Dominguez, Alma R.
Format:	Journal Article
Language:	English
Published:	Hangzhou Zhejiang University Press 2021 Springer Nature B.V Automatic Control Department, CINVESTAV, Mexico City 07360, Mexico%The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague 18200, Czech Republic%Biotechnology and Bioengineering Department, CINVESTAV, Mexico City 07360, Mexico
Subjects:	Adaptation Bioreactors Communications Engineering Computer Hardware Computer Science Computer Systems Organization and Communication Networks Dynamical systems Electrical Engineering Electronics and Microelectronics Instrumentation Kalman filters Linear matrix inequalities Mathematical analysis Networks Nonlinear systems Observers Pollutants Wastewater treatment Water treatment Adaptive observers Nonlinear observers Pollutant observation Chemostat TP273 Coordinate change
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Summary:	This study deals with constant-gain adaptive observers for nonlinear systems, for which relatively few solutions are available for some particular cases. We introduce an asymptotic observer of constant gain for nonlinear systems that have linear input. This allows the observer design to be formulated within the linear matrix inequality paradigm provided that a strictly positive real condition between the input disturbance and the output is fulfilled. The proposed observer is then applied to a large class of nonlinear chemostat dynamical systems that are widely used in the fermentation process, cell cultures, medicine, etc. In fact, under standard practical assumptions, the necessary change of the chemostat state coordinates exists, allowing use of the constant-gain observer. Finally, the developed theory is illustrated by estimating pollutant concentration in a Spirulina maxima wastewater treatment facility.
ISSN:	2095-9184 2095-9230
DOI:	10.1631/FITEE.2000368