Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Bezglasnyi S. P., Kurkina E. V. Construction and Stabilization Program Motions of Nonautonomous Hamiltonian Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 3, pp. 74-80. DOI: 10.18500/1816-9791-2011-11-3-2-74-80

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.08.2011
Full text:
download
(downloads: 142)
Language: 
Russian
Heading: 
Mechanics
UDC: 
62.534(031)
DOI: 
10.18500/1816-9791-2011-11-3-2-74-80

Construction and Stabilization Program Motions of Nonautonomous Hamiltonian Systems

Autors: 
Bezglasnyi Sergey Pavlovich, Samara National Research University
Kurkina E. V., Samara National Research University
Abstract: 

We consider program motion of Hamiltonian system and solve the problem of construction asymptotically stability programm motion. The programm motion can be any function. Control is received in the method and the method of limiting functions and systems. In this case we use the Lyapunov’s functions having constant signs derivatives. The following examples are considered: stabilization of program motions of homogeneous rod of variable length and stabilization of program motions of mathematical pendulum variable length in the rotation plane.

Key words: 
Hamiltonian
nonautonomous system
program motion
Lyapunov’s function
References: 
  1. Летов А. М. Динамика полета и управление. М.: Наука, 1969. 359 с.
  2. Галиуллин А. С., Мухаметзянов И. А., Мухарлямов Р. Г., Фурасов В. Д. Построение систем программного движения. М.: Наука, 1971. 352 с.
  3. Зубов В. И. Проблема устойчивости процессов управления. Л.: Судостроение, 1980. 375 с.
  4. Афанасьев В. Н., Колмановский В. Б., Носов В. Р. Математическая теория конструирования систем управления. М.: Высш. шк., 1989. 447 с.
  5. Малкин И. Г. Теория устойчивости движения. М.: Наука, 1966. 530 с.
  6. Artstein Z. Topological dynamics of an ordinary equations // J. Differ. Equat. 1977. Vol. 23. P. 216–223.
  7. Андреев А. С. Об устойчивости и неустойчивости нулевого решения неавтономной системы // ПММ. 1984. Вып. 2. С. 40–45.
  8. Bezglasnyi S. P. The stabilization of equilibrium state of nonlinear hamiltonian systems // Seminarberichte aus dem Fachberrich Mathematik. FernUnivetsitat in Hagen. ̈ 2001. Bd. 71. P. 45–53.
  9. Маркеев А. П. Теоретическая механика. М.: Физмалит, 1990. 414 с.
  10. Bezglasnyi S. P. The stabilization of program motions of controlled nonlinear mechanical systems // Korean J. Comput. and Appl. Math. 2004. Vol. 14, No 1. P. 251–266.
  • 798 reads