A time-delay equation: well-posedness to optimal control

Open Physics

Alkan Sertan¹  Yildirim Kenan² 

[1] Department of Mathematics, Mustafa Kemal University, Hatay, Turkey;Mus Alparslan University, Mus, Turkey;

关键词: wellposedness;    time-delay;    vibration;    control;    maximum principle;    64.30.ef;    62.20.dj;    62.20.fg;    62.30.+d;   

DOI  :  10.1515/phys-2016-0026

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown