Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

Russian Russian English English About Journal | Issues | Editorial Board | Contact Us
 


IssuesArchive of Issues2008-3pp.270-278

Archive of Issues

Total articles in the database: 10522
In Russian (ΟΜΜ): 9723
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 72, Issue 3 / 2008 | Next article >>
A.N. Sirotin, "The existence of smooth solutions in a problem of the optimal control of the rotation of an axisymmetric rigid body," J. Appl. Math. Mech. 72 (3), 270-278 (2008)
Year 2008 Volume 72 Issue 3 Pages 270-278
Title The existence of smooth solutions in a problem of the optimal control of the rotation of an axisymmetric rigid body
Author(s) A.N. Sirotin (Moscow, Russia, asirotin2@yandex.ru)
Abstract The problem of the existence of a solution in the problem of the optimal control of the rotation of an axisymmetric rigid body for the arbitrary case of angular velocity boundary conditions is studied. A square integrable functional, which is consistent with the symmetry of the rotating body and characterizes the power consumption, is chosen as the criterion. The principal moment of the applied external forces serves as the control and the time of termination of a manoeuvre can be both specified as well as free. In the case of a specified termination time, it is shown that the solution (control) belongs to the class of infinitely-differentiable functions of time. The reasoning is based on the use of the singularities of the structure of the differential equations and the possibility of reducing the initial problem to two successive variational problems. The existence of a solution of the first of these problems in the class of square integrable functions is proved using the Cauchy-Bunyakovskii inequality. The second problem reduces to a search for the minimum of a functional which is weakly lower semi-continuous on a weakly compact set and the existence of its solution in the same class of functions follows from the Weierstrass theorem. The required conclusion concerning the smoothness of the solution of the optimal control problem is obtained from the necessary conditions of Pontryagin's maximum principle. In the case of a free termination time, one of the minimizing sequence can be constructed and it can be shown that, in the general case, there is no solution in the class of measurable controls.
Received 16 May 2007
Link to Fulltext
<< Previous article | Volume 72, Issue 3 / 2008 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru https://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Journal of Applied Mathematics and Mechanics
webmaster
Rambler's Top100