scholarly journals Optimal Control Problem for Some Degenerate Variation Inequality: Attainability Problem

2018 ◽  
Vol 26 (2) ◽  
pp. 37 ◽  
Author(s):  
Nina V. Kasimova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variation Inequality

scholarly journals H-solvability of optimal control problem for degenerate parabolic variation inequality

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Nina Vasylivna Kasimova
Keyword(s):  
Optimal Control ◽  
Differential Operator ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Direct Method ◽  
Control Space ◽  
Admissible Pairs ◽  
Degenerate Parabolic ◽  
Variation Inequality ◽  
Admissible Solutions

We consider the optimal control problem for  degenerate parabolic variation inequality with weight function of potential type that is in differential operator. Using the direct method of calculus of variations we prove the solvability of mentioned above optimal control problem in the class of so-called H-admissible solutions. It is also established that the set of H-admissible pairs is closed in the product of topologies of the state space and the control space.

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.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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