Publication detail
A PROBLEM OF FUNCTIONAL MINIMIZING FOR SINGLE DELAYED DIFFERENTIAL SYSTEM
DEMCHENKO, H. DIBLÍK, J.
Original Title
A PROBLEM OF FUNCTIONAL MINIMIZING FOR SINGLE DELAYED DIFFERENTIAL SYSTEM
English Title
A PROBLEM OF FUNCTIONAL MINIMIZING FOR SINGLE DELAYED DIFFERENTIAL SYSTEM
Type
conference paper
Language
en
Original Abstract
In the contribution, a linear differential system with a single delay $$ \frac{dx(t)}{dt} =A_{0} x(t)+A_{1} x(t-\tau)+bu(t), t\ge t_{0} $$ where $A_{0}$, $A_{1}$ are $n\times n$ constant matrices, $x\in R^{n}$, $b\in R^{n}$, $\tau>0$, $t_0\in{\mathbb{R}}$, $u\in R$, is considered. A problem of minimizing (by a suitable control function $u(t)$) a functional \begin{multline*} I=\int _{t_0}^{\infty }(x^{T}(t)C_{11}x(t)+x^{T}(t)C_{12} x(t-\tau) \\ +x^{T}(t-\tau)C_{21}x(t)+x^{T}(t-\tau)C_{22}x(t-\tau)+du^{2}(t))\mathrm{d}t, \end{multline*} where $C_{11}$, $C_{12}$, $C_{21}$, $C_{22}$ are $n\times n$ constant matrices, $d>0$, and the integrand is a positive-definite quadratic form, is considered. To solve the problem, Malkin's approach and Lyapunov's second method are utilized
English abstract
In the contribution, a linear differential system with a single delay $$ \frac{dx(t)}{dt} =A_{0} x(t)+A_{1} x(t-\tau)+bu(t), t\ge t_{0} $$ where $A_{0}$, $A_{1}$ are $n\times n$ constant matrices, $x\in R^{n}$, $b\in R^{n}$, $\tau>0$, $t_0\in{\mathbb{R}}$, $u\in R$, is considered. A problem of minimizing (by a suitable control function $u(t)$) a functional \begin{multline*} I=\int _{t_0}^{\infty }(x^{T}(t)C_{11}x(t)+x^{T}(t)C_{12} x(t-\tau) \\ +x^{T}(t-\tau)C_{21}x(t)+x^{T}(t-\tau)C_{22}x(t-\tau)+du^{2}(t))\mathrm{d}t, \end{multline*} where $C_{11}$, $C_{12}$, $C_{21}$, $C_{22}$ are $n\times n$ constant matrices, $d>0$, and the integrand is a positive-definite quadratic form, is considered. To solve the problem, Malkin's approach and Lyapunov's second method are utilized
Keywords
delayed differential system, Lyapunov-Krasovskii functional, integral quality criterion, optimal control.
Released
15.06.2017
Publisher
University of Defence
Location
Brno
ISBN
978-80-7582-026-6
Book
Mathematics, Information Technologies and Applied Sciences 2017
Edition number
1
Pages from
55
Pages to
62
Pages count
8
URL
Documents
BibTex
@inproceedings{BUT142612,
author="Hanna {Demchenko} and Josef {Diblík}",
title="A PROBLEM OF FUNCTIONAL MINIMIZING FOR SINGLE DELAYED DIFFERENTIAL SYSTEM",
annote="In the contribution, a linear differential system with a single delay
$$
\frac{dx(t)}{dt} =A_{0} x(t)+A_{1} x(t-\tau)+bu(t), t\ge t_{0}
$$
where $A_{0}$, $A_{1}$ are $n\times n$ constant matrices, $x\in R^{n}$, $b\in R^{n}$, $\tau>0$, $t_0\in{\mathbb{R}}$,
$u\in R$, is considered.
A problem of minimizing (by a suitable control function $u(t)$) a functional
\begin{multline*}
I=\int _{t_0}^{\infty }(x^{T}(t)C_{11}x(t)+x^{T}(t)C_{12} x(t-\tau)
\\
+x^{T}(t-\tau)C_{21}x(t)+x^{T}(t-\tau)C_{22}x(t-\tau)+du^{2}(t))\mathrm{d}t,
\end{multline*}
where $C_{11}$, $C_{12}$, $C_{21}$, $C_{22}$ are $n\times n$ constant matrices, $d>0$,
and the integrand is a positive-definite quadratic form,
is
considered. To solve the problem, Malkin's approach and
Lyapunov's second method are utilized",
address="University of Defence",
booktitle="Mathematics, Information Technologies and Applied Sciences 2017",
chapter="142612",
howpublished="online",
institution="University of Defence",
year="2017",
month="june",
pages="55--62",
publisher="University of Defence",
type="conference paper"
}