Publication detail
Optimal Control by Lyapunov's Direct Method
DEMCHENKO, H. DIBLÍK, J. KHUSAINOV, D.
Original Title
Optimal Control by Lyapunov's Direct Method
English Title
Optimal Control by Lyapunov's Direct Method
Type
abstract
Language
en
Original Abstract
Two approaches to solving optimization problems of dynamic systems are well-known. The first approach needs to find a fixed control (program control) for which the system described by differential equations reaches a predetermined value and minimizes an integral quality criterion. Proposed by L.S. Pontryagin, this method was in essence a further development of general optimization methods for dynamical systems. The second method consists in finding a control function (in the form of a feedback) guaranteeing that, simultaneously, the zero solution is asymptotically stable and an integral quality criterion attains a minimum value. This method is based on what is called the second Lyapunov method and its founder is N.N. Krasovskii. In the paper, the latter method is applied to linear differential equations and systems with integral quality criteria.
English abstract
Two approaches to solving optimization problems of dynamic systems are well-known. The first approach needs to find a fixed control (program control) for which the system described by differential equations reaches a predetermined value and minimizes an integral quality criterion. Proposed by L.S. Pontryagin, this method was in essence a further development of general optimization methods for dynamical systems. The second method consists in finding a control function (in the form of a feedback) guaranteeing that, simultaneously, the zero solution is asymptotically stable and an integral quality criterion attains a minimum value. This method is based on what is called the second Lyapunov method and its founder is N.N. Krasovskii. In the paper, the latter method is applied to linear differential equations and systems with integral quality criteria.
Keywords
Lyapunov function, optimization problem, integral quality criterion, control function
Released
27.05.2015
ISBN
978-617-571-116-3
Book
Dynamical System Modelling and Stability Investigation
Pages from
137
Pages to
137
Pages count
1
Documents
BibTex
@misc{BUT119176,
author="Hanna {Demchenko} and Josef {Diblík} and Denys {Khusainov}",
title="Optimal Control by Lyapunov's Direct Method",
annote="Two approaches to solving optimization problems of dynamic systems are well-known.
The first approach needs to find a fixed control (program control) for which the system described
by differential equations reaches a predetermined value and minimizes an integral quality criterion.
Proposed by L.S. Pontryagin, this method was in essence a further development of general optimization
methods for dynamical systems. The second method consists in finding a control function (in
the form of a feedback) guaranteeing that, simultaneously, the zero solution is asymptotically stable
and an integral quality criterion attains a minimum value. This method is based on what is called
the second Lyapunov method and its founder is N.N. Krasovskii. In the paper, the latter method is
applied to linear differential equations and systems with integral quality criteria.",
booktitle="Dynamical System Modelling and Stability Investigation",
chapter="119176",
howpublished="print",
year="2015",
month="may",
pages="137--137",
type="abstract"
}