An existence theorem for a fractional control problem

1973 ◽  
Vol 11 (4) ◽  
pp. 379-385 ◽  
Author(s):  
S. K. Bhatt
Keyword(s):  
Control Problem ◽  
Existence Theorem ◽  
Fractional Control

scholarly journals The existence theorem for weak solution of optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions

2019 ◽  
Vol 488 (2) ◽  
pp. 133-136
Author(s):  
P. I. Plotnikov ◽  
M. V. Turbin ◽  
A. S. Ustiuzhaninova
Keyword(s):  
Weak Solution ◽  
Feedback Control ◽  
Control Problem ◽  
Existence Theorem ◽  
Polymer Solutions ◽  
Optimal Feedback Control ◽  
Operator Inclusion ◽  
Optimal Feedback ◽  
Aqueous Polymer ◽  
Voigt Model

In this paper the existence theorem on weak solution of the optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions. The proof is carried out on the basis of an approximation-topological approach to the study of fluid dynamic problems. At the first step, the considered feedback control problem is interpreted as an operator inclusion with a multi-valued right-hand side. In the second step, the resulting inclusion is approximated by an operator inclusion with better properties. Then, on the basis of a priori estimates of solutions and the degree theory of a class of multi-valued mappings, the existence of solutions for this inclusion is proved. In the third step, it is shown that from the sequence of solutions of the approximation inclusion one can extract a subsequence that converges weakly to the solution of the original inclusion. Then it is proved that among the solutions of the considered problem there is a solution that gives a minimum to a given quality functional.

scholarly journals OPTIMAL CONTROL FOR SYSTEMS GOVERNED BY DISCONTINUOUS NONLINEARITY

1999 ◽  
Vol 30 (4) ◽  
pp. 289-294
Author(s):  
NGUYEN BUONG
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Theoretical Result ◽  
Control Problem ◽  
Existence Theorem ◽  
Integral Equations ◽  
Operator Equation ◽  
Nonlinear Operator ◽  
Discontinuous Nonlinearity ◽  
Nonlinear Integral Equations

The aim of this paper is to present an existence theorem of optimal control for systems descrided by the operator equation of Hammerstein type $x + K F(u, x) = 0$ with the discontinuous monotone nonlinear operator $F$ in $x$. Then, the theoretical result is applied to investigate an optimal control problem for system, where the state is written in the form of nonlinear integral equations in $L_p(\omega)$.

An optimal control problem in exterior hydrodynamics

1992 ◽  
Vol 121 (1-2) ◽  
pp. 5-32 ◽  
Author(s):  
S. S. Sritharan
Keyword(s):  
Optimal Control ◽  
Energy Expenditure ◽  
Optimal Control Problem ◽  
Viscous Fluid ◽  
Control Problem ◽  
Existence Theorem ◽  
Minimum Energy ◽  
Reynolds Numbers ◽  
Incompressible Viscous Fluid ◽  
Absolute Minimum

SynopsisIn this paper we consider the problem of accelerating an obstacle in an incompressible viscous fluid from rest to a given speed in a given time with minimum energy expenditure. An existence theorem for the speed trajectory which corresponds to the absolute minimum is provided. The results are valid for arbitrary Reynolds numbers.

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.

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