An optimal control problem with nonlocal conditions for the weakly nonlinear hyperbolic equation

2012 ◽  
Vol 34 (2) ◽  
pp. 216-235 ◽  
Author(s):  
H.F. Guliyev ◽  
H.T. Tagiyev
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic Equation ◽  
Nonlocal Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Weakly Nonlinear

scholarly journals Necessary optimality condition for the singular controls in an optimal control problem with nonlocal conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 749-757
Author(s):  
Ali Safari ◽  
Yagub Sharifov ◽  
Yusif Gasimov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlocal Conditions ◽  
Integral Boundary Conditions ◽  
Necessary Optimality Condition ◽  
Integral Boundary ◽  
Singular Controls ◽  
The Cauchy Problem ◽  
Continue Investigation

In this paper, we continue investigation of the problem considered in our earlier works. The paper deals with an optimal control problem for an ordinary differential equation with integral boundary conditions that generalizes the Cauchy problem. The problem is investigated the case when Pontryagin?s maximum principle is degenerate. Moreover, the second order optimality conditions are derived for the considered problem.

scholarly journals The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

2020 ◽  
Vol 13 (2) ◽  
pp. 314-322
Author(s):  
Gunay Ismayilova
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Necessary Condition ◽  
Weakly Nonlinear ◽  
Necessary Condition Of Optimality

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

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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