scholarly journals On the solvability of the tracking problem in the optimization of the thermal process by moving point controls

2021 ◽  
Vol 102 (2) ◽  
pp. 67-73
Author(s):  
A. Kerimbekov ◽  
◽  
A.T. Ermekbaeva ◽  
E. Seidakmat kyzy ◽  
◽  
...  
Keyword(s):  
Control Function ◽  
Complete Solution ◽  
Sufficient Conditions ◽  
Point Sources ◽  
Thermal Processes ◽  
Optimal Controls ◽  
Tracking Problem ◽  
Point Control ◽  
Linear Integral ◽  
Linear Integral Equations

In the present article we investigate problems of tracking in the moving point control of thermal processes described by Fredholm integro-differential equations in partial derivatives with the Fredholm integral operator, in the case when the functions of point sources are nonlinear with respect to the control function. It is found that optimal controls are defined as solutions to a system of linear integral equations, and an algorithm for constructing its solution is developed. Sufficient conditions for the unique solvability of the tracking problem are found and an algorithm for constructing a complete solution to the nonlinear optimization problem was indicated.

PRINCIPLE AND THEOREMS OF REVERSIONAL CALCULATION

2021 ◽  
Vol 3 ◽  
pp. 12-20
Author(s):  
A.I. BOKHONSKY ◽  
N.I. VARMINSKAYA ◽  
A.I. RYZHKOV
Keyword(s):  
Control Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Analytical Control ◽  
Optimal Controls ◽  
Initial State ◽  
Numerical Equality ◽  
Special Cases ◽  
Controlled Motion ◽  
State Of Rest

A reverse optimality principle (ROP) is formulated and an algorithm for its use for constructing optimal portable object movements is presented. Using an example, sufficient conditions for the extremality of the restored criterion functional are verified when constructing an optimal control of the «acceleration–deceleration» type. The following theorems were formulated and proved: on the numerical equality of integrals with different integral functions, on the minimum energy to achieve the goal of optimally controlled motion in the form of «acceleration–deceleration». Basing on the generalization of the results for optimal controls designing of the «acceleration–deceleration» type of motion, whence the known special cases follow, universal analytical control function (translational acceleration) was found. Analytically and numerically was confirmed the existence of the limiting minimum control energy at which the movement of an object from the initial state of rest to a new state of rest is possible at a fixed distance and time of motion.

Model-based HSF using by target point control function

2015 ◽  
Author(s):  
Seongjin Kim ◽  
Munhoe Do ◽  
Yongbae An ◽  
Jaeseung Choi ◽  
Hyunjo Yang ◽  
...  
Keyword(s):  
Control Function ◽  
Target Point ◽  
Model Based ◽  
Point Control

scholarly journals First and second order optimality conditions for the control of Fokker-Planck equations

2021 ◽  
Vol 27 ◽  
pp. 15
Author(s):  
M. Soledad Aronna ◽  
Fredi Tröltzsch
Keyword(s):  
Control Variable ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Second Order ◽  
Optimal Controls ◽  
Main Emphasis ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0 The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

scholarly journals On Solvability Conditions for a Certain Conjugation Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 234
Author(s):  
Vladimir Vasilyev ◽  
Nikolai Eberlein
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Mellin Transform ◽  
Algebraic Equations ◽  
Conjugation Problem ◽  
Solvability Conditions ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

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