# A nonlinear plate control without linearization

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 179-186
• ISSN: 2391-5455

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## Abstract

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In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

## How to cite

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Kenan Yildirim, and Ismail Kucuk. "A nonlinear plate control without linearization." Open Mathematics 15.1 (2017): 179-186. <http://eudml.org/doc/288068>.

@article{KenanYildirim2017,
abstract = {In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.},
author = {Kenan Yildirim, Ismail Kucuk},
journal = {Open Mathematics},
keywords = {Nonlinear plate; Optimality; Vibration; Maximum principle; nonlinear plate; optimality; vibration; maximum principle},
language = {eng},
number = {1},
pages = {179-186},
title = {A nonlinear plate control without linearization},
url = {http://eudml.org/doc/288068},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Kenan Yildirim
AU - Ismail Kucuk
TI - A nonlinear plate control without linearization
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 179
EP - 186
AB - In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.
LA - eng
KW - Nonlinear plate; Optimality; Vibration; Maximum principle; nonlinear plate; optimality; vibration; maximum principle
UR - http://eudml.org/doc/288068
ER -

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