State estimation for miso non-linear systems in controller canonical form

Benoît Schwaller; Denis Ensminger; Birgitta Dresp-Langley; José Ragot

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 3, page 569-583
  • ISSN: 1641-876X

Abstract

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We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

How to cite

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Benoît Schwaller, et al. "State estimation for miso non-linear systems in controller canonical form." International Journal of Applied Mathematics and Computer Science 26.3 (2016): 569-583. <http://eudml.org/doc/286726>.

@article{BenoîtSchwaller2016,
abstract = {We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.},
author = {Benoît Schwaller, Denis Ensminger, Birgitta Dresp-Langley, José Ragot},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {non-linear systems; state observers; continuous time},
language = {eng},
number = {3},
pages = {569-583},
title = {State estimation for miso non-linear systems in controller canonical form},
url = {http://eudml.org/doc/286726},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Benoît Schwaller
AU - Denis Ensminger
AU - Birgitta Dresp-Langley
AU - José Ragot
TI - State estimation for miso non-linear systems in controller canonical form
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 3
SP - 569
EP - 583
AB - We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
LA - eng
KW - non-linear systems; state observers; continuous time
UR - http://eudml.org/doc/286726
ER -

References

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