Controller design for bush-type 1-d wave networks∗

Yaxuan Zhang; Genqi Xu

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 1, page 208-228
  • ISSN: 1292-8119

Abstract

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In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s lemma and semigroup theory. The validity of cutting-edge method is proved by spectral analysis approach. In particular, we give a detailed procedure of cutting-edge for the bush-type wave networks. The results show that if we impose feedback controllers, consisting of velocity and position terms, at all the boundary vertices and at most three velocity feedback controllers on the cycle, the system is asymptotically stabilized. Finally, some examples are given.

How to cite

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Zhang, Yaxuan, and Xu, Genqi. "Controller design for bush-type 1-d wave networks∗." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 208-228. <http://eudml.org/doc/277823>.

@article{Zhang2012,
abstract = {In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s lemma and semigroup theory. The validity of cutting-edge method is proved by spectral analysis approach. In particular, we give a detailed procedure of cutting-edge for the bush-type wave networks. The results show that if we impose feedback controllers, consisting of velocity and position terms, at all the boundary vertices and at most three velocity feedback controllers on the cycle, the system is asymptotically stabilized. Finally, some examples are given. },
author = {Zhang, Yaxuan, Xu, Genqi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Bush-type; wave network; controller design; asymptotic stability; cutting-edge; number and locations of the controllers},
language = {eng},
month = {2},
number = {1},
pages = {208-228},
publisher = {EDP Sciences},
title = {Controller design for bush-type 1-d wave networks∗},
url = {http://eudml.org/doc/277823},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Zhang, Yaxuan
AU - Xu, Genqi
TI - Controller design for bush-type 1-d wave networks∗
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/2//
PB - EDP Sciences
VL - 18
IS - 1
SP - 208
EP - 228
AB - In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s lemma and semigroup theory. The validity of cutting-edge method is proved by spectral analysis approach. In particular, we give a detailed procedure of cutting-edge for the bush-type wave networks. The results show that if we impose feedback controllers, consisting of velocity and position terms, at all the boundary vertices and at most three velocity feedback controllers on the cycle, the system is asymptotically stabilized. Finally, some examples are given.
LA - eng
KW - Bush-type; wave network; controller design; asymptotic stability; cutting-edge; number and locations of the controllers
UR - http://eudml.org/doc/277823
ER -

References

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