# A nonlinear plate control without linearization

Open Mathematics (2017)

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

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topKenan 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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