A Novel Proof on the Existence of the Solution of Fractional Control Problem Governed by Burgers Equations

2019 ◽  
Vol 32 (2) ◽  
pp. 129-143 ◽  
Author(s):  
S. G. Georgiev sci
Keyword(s):  
Control Problem ◽  
Burgers Equations ◽  
Fractional Control

scholarly journals Harvest Management Problem with a Fractional Logistic Equation

2021 ◽  
Author(s):  
Melani Barrios ◽  
Gabriela Reyero ◽  
Mabel Tidball
Keyword(s):  
Control Problem ◽  
Numerical Simulations ◽  
Classical Case ◽  
Logistic Equation ◽  
Management Problem ◽  
Harvest Management ◽  
Fractional Control

In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. We perform several numerical simulations to make a comparison between both cases.

An optimal control problem associated to a class of fractional Burgers’ equations

2019 ◽  
Vol 13 (04) ◽  
pp. 2050079
Author(s):  
F. Mohammadizadeh ◽  
H. A. Tehrani ◽  
S. G. Georgiev ◽  
M. H. Noori Skandari
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Unique Solution ◽  
Special Class ◽  
Optimal Solution ◽  
Burgers Equations

In this paper, we prove that a class of fractional Burgers’ equations has a unique solution under some special conditions. Moreover, we show that an optimal control problem for a special class of fractional Burgers’ equations has at least one optimal solution.

Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem

2020 ◽  
Vol 26 ◽  
pp. 78
Author(s):  
Thirupathi Gudi ◽  
Ramesh Ch. Sau
Keyword(s):  
Finite Element ◽  
Control Problem ◽  
Dirichlet Boundary ◽  
A Priori ◽  
Diffusion Problem ◽  
Discrete Control ◽  
Optimal Order ◽  
Control Constraints ◽  
Element Analysis ◽  
Dirichlet Boundary Control

We study an energy space-based approach for the Dirichlet boundary optimal control problem governed by the Laplace equation with control constraints. The optimality system results in a simplified Signorini type problem for control which is coupled with boundary value problems for state and costate variables. We propose a finite element based numerical method using the linear Lagrange finite element spaces with discrete control constraints at the Lagrange nodes. The analysis is presented in a combination for both the gradient and the L2 cost functional. A priori error estimates of optimal order in the energy norm is derived up to the regularity of the solution for both the cases. Theoretical results are illustrated by some numerical experiments.

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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