A time-delay equation: well-posedness to optimal control
Yükleniyor...
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
De Gruyter Open Ltd
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a time-delayed distributed parameter system(DPS) and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem. The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.
Açıklama
Anahtar Kelimeler
Wellposedness, Time-delay, Vibration, Control, Maximum Principle
Kaynak
Open Physics
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
14
Sayı
1
