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

TORRES Jorge A.; SONCK Arno; ČELIKOVSKY Sergej; DOMINGUEZ Alma R.

doi:10.1631/FITEE.2000368

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

Special Issue on Distributed Filtering and Control of Complex Networks and Systems | Updated：2022-05-19

- Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems
- 再论常增益非线性自适应观测器：恒化器系统的应用
- Frontiers of Information Technology & Electronic Engineering Vol. 22, Issue 1, Pages: 68-78(2021)
- Affiliations：
  
  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
- Author bio：
  
  [ "Jorge A. TORRES, E-mail: jtorres@ctrl.cinvestav.mx" ]
  [ "Arno SONCK, E-mail: gsonck@ctrl.cinvestav.mx" ]
  Sergej ČELIKOVSKY, E-mail: celikovs@utia.cas.cz
  [ "Alma R. DOMINGUEZ, E-mail: adomin@cinvestav.mx" ]
- Funds：
- DOI：10.1631/FITEE.2000368
  CLC： TP273
- Received：22 July 2020，
  
  Revised：2020-11-11，
  
  Published：2021-01
- Accepted：
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TORRES Jorge A., SONCK Arno, ČELIKOVSKY Sergej, et al. Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(1): 68-78.
DOI：

TORRES Jorge A., SONCK Arno, ČELIKOVSKY Sergej, et al. Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(1): 68-78. DOI： 10.1631/FITEE.2000368.

摘要

本文研究非线性系统的常增益自适应观测器；对一些特殊情况，有效的解决方案很少。针对具有线性输入的非线性系统，介绍一种常增益渐近观测器，使得当输入扰动和输出间满足严格正实的条件时，可以利用线性矩阵不等式工具设计观测器。所设计的观测器被应用于一大类非线性恒化动态系统，这类系统广泛应用于发酵工艺、细胞培养、医学等。事实上，基于标准的实际假设，存在必要的恒化器状态坐标变换，允许运用常增益观测器。最后，利用极大螺旋藻污水处理设施中估计污染物浓度的例子验证所提理论方法。

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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Keywords

references

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