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

Abstract

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.

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Authors

Corresponding author

Correspondence to Sergej Čelikovský.

Additional information

This research was partly supported by the Czech Science Foundation (No. GA19-05872S)

Contributors

Jorge A. TORRES and Sergej ČELIKOVSKÝ conceptualized the research. Arno SONCK developed the theoretical findings of the work. Arno SONCK and Alma R. DOMINGUEZ contributed to the design and simulation of the experiment results. Arno SONCK and Jorge A. TORRES drafted the manuscript. Sergej ČELIKOVSKÝ revised and finalized the paper.

Compliance with ethics guidelines

Jorge A. TORRES, Arno SONCK, Sergej ČELIKOVSKÝ, and Alma R. DOMINGUEZ declare that they have no conflict of interest.

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Torres, J.A., Sonck, A., Čelikovský, S. et al. Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems. Front Inform Technol Electron Eng 22, 68–78 (2021). https://doi.org/10.1631/FITEE.2000368

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Key words

  • Nonlinear observers
  • Adaptive observers
  • Coordinate change
  • Chemostat
  • Pollutant observation

CLC number

  • TP273