A nonlinear plate control without linearization

• Autorzy: Kenan Yildirim , Ismail Kucuk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nonlinear plate; Optimality; Vibration; Maximum principle

Kategorie tematyczne

• 35Q93: PDEs in connection with control and optimization
• 74H45: Vibrations
• 49N05: Linear optimal control problems
• 49J20: Optimal control problems involving partial differential equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 179-186

Daty

wydano

2017-01-01

otrzymano

2016-07-29

zaakceptowano

2016-10-10

online

2017-03-08

Twórcy

autor

Kenan Yildirim

• Mus Alparslan University, Mus,

autor

Ismail Kucuk

• Yildiz Technical University, Istanbul,

Identyfikatory

DOI

10.1515/math-2017-0011