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"
}