Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Pankratov I. A. Using Galerkin Method for Solving Linear Optimal Control Problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 340-349. DOI: 10.18500/1816-9791-2014-14-3-340-349, EDN: SMSJYN

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
10.09.2014
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Language: 
Russian
Heading: 
Mechanics
UDC: 
519.6, 531
DOI: 
10.18500/1816-9791-2014-14-3-340-349
EDN: 
SMSJYN

Using Galerkin Method for Solving Linear Optimal Control Problems

Autors: 
Pankratov Il'ya Alekseevich, Saratov State University
Abstract: 

The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given.

Key words: 
optimal control
linear system
Galerkin method
References: 
  1. Pontriagin L. S., Boltianskii V. G., Gamkrelidze R. V.,Mishchenko E. F. Matematicheskaia teoriia optimal’nykh protsessov [The mathematical theory of optimal processes]. Moscow, Nauka, 1983, 393 p. (in Russian).
  2. Roitenberg Ya. N. Avtomaticheskoe upravlenie [Automatic control]. Moscow, Nauka, 1983, 393 p. (in Russian).
  3. Moiseev N. N. Chislennye metody v teorii optimal’nykh sistem [Numerical methods in the theory of optimal systems]. Moscow, Nauka, 1971, 424 p. (in Russian).
  4. Fedorenko R. P. Priblizhennoe reshenie zadach optimal’nogo upravleniia [Approximate solution of optimal control problems]. Moscow, Nauka, 1978, 488 p. (in Russian).
  5. Vasil’ev F. P. Chislennye metody resheniia ekstremal’nykh zadach [Numerical methods for solving extrema problems]. Moscow, Nauka, 1988, 552 p. (in Russian).
  6. Zienkiewicz O., Morgan K. Finite elements and approximation. New York, Chichester, Brisbane, Toronto, John Wiley and Sons, 1983, 328 p.
  7. Pankratov I. A., Sapunkov Ya. G., Chelnokov Yu. N. About a problem of spacecraft’s orbit optimal reorientation. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2012, vol. 12, iss. 3, pp. 87–95 (in Russian).
  8. Pankratov I. A., Sapunkov Ya. G., Chelnokov Yu. N. Solution of a problem of spacecraft’s orbit optimal reorientation using quaternion equations of orbital system of coordinates orientation. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 1, pt. 1, pp. 87–95 (in Russian).
  9. Chelnokov Yu. N. The use of quaternions in the optimal control problems of motion of the center of mass of a spacecraft in a newtonian gravitational field: III. Cosmic Research, 2003, vol. 41, no. 5, pp. 460-477. DOI 10.1023/A:1026098216710. 
Received: 
20.03.2014
Accepted: 
05.08.2014
Published: 
10.09.2014
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