# Adaptive compensators for perturbed positive real infinite-dimensional systems

Ruth Curtain; Michael Demetriou; Kazufumi Ito

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 4, page 441-452
- ISSN: 1641-876X

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topCurtain, Ruth, Demetriou, Michael, and Ito, Kazufumi. "Adaptive compensators for perturbed positive real infinite-dimensional systems." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 441-452. <http://eudml.org/doc/207656>.

@article{Curtain2003,

abstract = {The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates, and the convergence of the estimator error. For the case of a known periodic exogenous input we design an adaptive compensator which forces the system to converge to a unique periodic solution. We illustrate our approach with a delay example and a diffusion example for which we obtain convincing numerical results.},

author = {Curtain, Ruth, Demetriou, Michael, Ito, Kazufumi},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {adaptive controllers; positive real systems; infinite dimensional systems; adaptive observer; adaptive compensator; infinite-dimensional systems; stability; Lyapunov redesign method},

language = {eng},

number = {4},

pages = {441-452},

title = {Adaptive compensators for perturbed positive real infinite-dimensional systems},

url = {http://eudml.org/doc/207656},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Curtain, Ruth

AU - Demetriou, Michael

AU - Ito, Kazufumi

TI - Adaptive compensators for perturbed positive real infinite-dimensional systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 4

SP - 441

EP - 452

AB - The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates, and the convergence of the estimator error. For the case of a known periodic exogenous input we design an adaptive compensator which forces the system to converge to a unique periodic solution. We illustrate our approach with a delay example and a diffusion example for which we obtain convincing numerical results.

LA - eng

KW - adaptive controllers; positive real systems; infinite dimensional systems; adaptive observer; adaptive compensator; infinite-dimensional systems; stability; Lyapunov redesign method

UR - http://eudml.org/doc/207656

ER -

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