<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.</p></abstract>

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.

An adaptive observer design approach for a class of discrete-time nonlinear systems

krishnan.srinivasarengan@univ-lorraine.fr

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems...

An adaptive observer design approach for a class of discrete-time nonlinear systems

Publié en ligne: 31 mars 2018

Pages: 55 - 67

Reçu: 10 févr. 2017

Accepté: 09 août 2017

DOI: https://doi.org/10.2478/amcs-2018-0004

Mots clés
adaptive observer, joint state and parameter estimation, Takagi-Sugeno model, time-varying parameter estimation, sector nonlinearity transformation, discrete-time nonlinear systems

© by Krishnan Srinivasarengan

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An adaptive observer design approach for a class of discrete-time nonlinear systems

Publié en ligne: 31 mars 2018

Pages: 55 - 67

Reçu: 10 févr. 2017

Accepté: 09 août 2017

DOI: https://doi.org/10.2478/amcs-2018-0004

Mots clésadaptive observer, joint state and parameter estimation, Takagi-Sugeno model, time-varying parameter estimation, sector nonlinearity transformation, discrete-time nonlinear systems

© by Krishnan Srinivasarengan

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
adaptive observer, joint state and parameter estimation, Takagi-Sugeno model, time-varying parameter estimation, sector nonlinearity transformation, discrete-time nonlinear systems