scholarly journals On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load

1987 ◽  
Vol 32 (4) ◽  
pp. 315-331
Author(s):  
Igor Bock ◽  
Ivan Hlaváček ◽  
Ján Lovíšek
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Von Karman ◽  
Von Kármán

Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations

2018 ◽  
Vol 52 (3) ◽  
pp. 1137-1172
Author(s):  
Gouranga Mallik ◽  
Neela Nataraj ◽  
Jean-Pierre Raymond
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Error Estimates ◽  
Numerical Approximation ◽  
The State ◽  
Distributed Optimal Control ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Von Kármán

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Kármán equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed to discretize the state and adjoint variables. The control is discretized using piece-wise constant approximations. A priori error estimates are derived for the state, adjoint and control variables. Numerical results that justify the theoretical results are presented.

scholarly journals BILINEAR OPTIMAL CONTROL OF THE VELOCITY TERM IN A VON KÁRMÁN PLATE EQUATION

2013 ◽  
Vol 54 (4) ◽  
pp. 291-305
Author(s):  
JONG YEOUL PARK ◽  
SUN HYE PARK ◽  
YONG HAN KANG
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence Of Solutions ◽  
Plate Equation ◽  
Spatial Variables ◽  
Von Karman ◽  
Von Kármán Plate ◽  
Von Kármán ◽  
Objective Functional

AbstractWe consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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