scholarly journals Optimisation problem for some class of hybrid differential-difference systems with delay

2021 ◽  
pp. 6-17
Author(s):  
Michael P. Dymkov
Keyword(s):  
Optimal Control ◽  
Convex Sets ◽  
Control Function ◽  
Analytical Form ◽  
Integral Control ◽  
Difference Systems ◽  
Delayed Arguments ◽  
Linear Differential ◽  
Special Case ◽  
Zero Equilibrium

In the paper, the linear differential-difference dynamic systems with delayed arguments are considered. Such systems have a lot of application areas, in particular, processes with repetitive and learning structure. We apply the method of the separation hyperplane theorem for convex sets to establish optimality conditions for the control function to drive the trajectory to zero equilibrium state in the fastest possible way. For the special case of the integral control constraints, the proposed method is detailed to establish an analytical form of the optimal control function. The illustrative example is given to demonstrate the obtained results with the step-by-step calculation of the basic elements of the optimal control.

Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set

2020 ◽  
pp. 370-386
Author(s):  
Pavel D. Lebedev ◽  
Alexander A. Uspenskii
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Control Function ◽  
Extreme Points ◽  
Transversality Condition ◽  
Analytical Form ◽  
Singular Set ◽  
Entire Area ◽  
Target Set ◽  
Special Points

A planar velocity control problem with a disc indicatrix and a target set with a smooth boundary having finite discontinuities of second-order derivatives of coordinate functions is considered. We have studied pseudo-vertices-special points of the goal boundary that generate a singularity for the optimal control function. For non-stationary pseudo-vertices with discontinuous curvature, one-way markers are found, the values of which are necessary for analytical and numerical construction of branches of a singular set. It is proved that the markers lie on the border of the spectrum-the region of possible values. One of them is equal to zero, the other takes an invalid value -∞. In their calculation, asymptotic expansions of a nonlinear equation expressing the transversality condition are applied. Exact formulas for the extreme points of branches of a singular set are also obtained based on markers. An example of a control problem is presented, in which the constructive elements are obtained using the developed methods (pseudo-vertex, its markers, and the extreme point of a singular set), are sufficient to construct a singular set and an optimal result function in an explicit analytical form over the entire area of consideration.

Optimal control of linear differential-difference systems of neutral type

1989 ◽  
Vol 49 (6) ◽  
pp. 1835-1850 ◽  
Author(s):  
R. T. Yanushevsky
Keyword(s):  
Optimal Control ◽  
Neutral Type ◽  
Difference Systems ◽  
Linear Differential

Dynamics Response Control of a Mindlin-Type Beam

2017 ◽  
Vol 17 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Kenan Yildirim ◽  
Seda G. Korpeoglu ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Maximum Principle ◽  
Control Problem ◽  
Control Function ◽  
Initial Boundary ◽  
Response Control ◽  
Adjoint Variables ◽  
Dynamics Response ◽  
Optimal Control Function

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

scholarly journals Dynamical system of the growth of COVID-19 with controller

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dania Altulea ◽  
Rafida M. Elobaid
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Growth Rate ◽  
Dynamic System ◽  
Unique Solution ◽  
Population Dynamic ◽  
Integral Control ◽  
The Social ◽  
Social Separation ◽  
Strong Control

AbstractRecently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.

scholarly journals Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Thabet Abdeljawad (Maraaba) ◽  
Fahd Jarad ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Delayed Arguments

scholarly journals On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function

2016 ◽  
Vol 161 (1-2) ◽  
pp. 551-581 ◽  
Author(s):  
Maik Ringkamp ◽  
Sina Ober-Blöbaum ◽  
Sigrid Leyendecker
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Function ◽  
Mixed Integer ◽  
Time Transformation ◽  
Control Problems ◽  
Fixed Integer

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

On an optimal control problem with an integral functional of a rational control function

2009 ◽  
Vol 45 (11) ◽  
pp. 1621-1635 ◽  
Author(s):  
N. L. Grigorenko ◽  
D. V. Kamzolkin ◽  
L. N. Luk’yanova ◽  
D. G. Pivovarchuk
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Integral Functional ◽  
Rational Control
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