Detail publikačního výsledku

Optimization of linear differential systems by Lyapunov direct method

DEMCHENKO, H.

Original Title

Optimization of linear differential systems by Lyapunov direct method

English Title

Optimization of linear differential systems by Lyapunov direct method

Type

Paper in proceedings (conference paper)

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

Key words in English

Lyapunov function, optimization problem, integral quality criterion, control function

Authors

DEMCHENKO, H.

RIV year

2016

Released

23.04.2015

Location

Brno

ISBN

978-80-214-5148-3

Book

Proceedings of the 21st Conference STUDENT EEICT 2015

ISBN

NEUVEDENO

Pages from

511

Pages to

515

Pages count

5

Full text in the Digital Library

http://hdl.handle.net/

BibTex

@inproceedings{BUT114475,
  author="Hanna {Demchenko}",
  title="Optimization of linear differential systems by Lyapunov direct method",
  booktitle="Proceedings of the 21st Conference STUDENT EEICT 2015",
  year="2015",
  number="I.",
  pages="511--515",
  address="Brno",
  isbn="978-80-214-5148-3"
}