рус eng
«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 46

On Some Problems of Trajectory Beam Program Control. Part I

Author(s)
Dmitri A. Ovsyannikov1, Elena D. Kotina1

1St. Petersburg University, St. Petersburg, Russian Federation

Abstract
This paper deals with problems of program control of a trajectory beam. We investigate formulations that arise when considering problems of charged particle beams control, as well as, for example, in image processing. In applied problems, it is often necessary to investigate the problem of the gravity center control of some set or changing the density distribution of particles according to some given one. The functionals proposed in the paper can be effectively used for the velocity field constructing in various image processing, in particular, medical diagnostic images. In this paper, the problem of constructing a velocity field is considered as a control and optimization problem, and, unlike the previous works of the authors, macroparameters characterizing the objects under study are used in optimization. In the article, variations of the studied functionals are obtained and the necessary optimality conditions are given.
About the Authors

Dmitri A. Ovsyannikov, Dr. Sci. (Phys.–Math.), Prof., Saint Petersburg State University, St. Petersburg, 199034, Russian Federation, d.a.ovsyannikov@spbu.ru

Elena D. Kotina, Dr. Sci. (Phys.–Math.), Prof., Saint Petersburg State University, St. Petersburg, 199034, Russian Federation, e.kotina@spbu.ru

For citation
Ovsyannikov D. A., Kotina E. D. On Some Problems of Trajectory Beam Program Control. Part I. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 46, pp. 51–65. (in Russian) https://doi.org/10.26516/1997-7670.2023.46.51
Keywords
program control, velocity field, trajectory beam, functional variation, optimization, image processing
UDC
517.97
MSC
49K99
DOI
https://doi.org/10.26516/1997-7670.2023.46.51
References
  1. Zubov V.I. Dinamika upravlyayemykh sistem. [Dynamics of Control Systems]. Мoscow, Vysshaya Shkola Publ., 1982, 285 p. (in Russian)
  2. Gecha V., Zhilenev M., Fyodorov V., Khrychev D., Hudak Yu., Shatina A. Velocity field of image points in satellite imagery of planet’s surface. Russian Technological Journal, 2020, vol. 8, no. 1, pp. 97–109. https://doi.org/10.32362/2500-316X-2020-8-1-97-10914
  3. Kotina E.D., Ovsyannikov D.A. Mathematical model of joint optimization of programmed and perturbed motions in discrete systems. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, no. 2, pp. 213–224. http://doi.org/10.21638/11701/spbu10.2021.210 (In Russian)
  4. Krasovskiy A.A. Statisticheskaya teoriya perekhodnykh protsessov v sistemakh upravleniya. [Statistical theory of transient processes in control systems]. Moscow, Nauka Publ., 1968, 240 p. (in Russian)
  5. Ovsyannikov D.A. Matematicheskie metody upravlenija puchkami. [Mathematical methods of beam control]. Leningrad, Leningrad University Publ., 1980, 228 p. (in Russian)
  6. Ovsyannikov D.A. Modelling and optimization of charged particle beam dynamics. Leningrad, Leningrad University Publ., 1990, 312 p. (in Russian)
  7. Barron J., Fleet D. Performance of optical flow techniques. International Journal of Computer Vision, 1994, vol. 12, pp. 43–77.
  8. Bazhanov P., Kotina E., Ovsyannikov D., Ploskikh V. Optimization algorithm of the velocity field determining in image processing. Cybernetics and Physics, 2018, vol. 7, pp. 174–181.
  9. Bruhn A., Weickert J., Schnorr C. Lucas/Kanade Meets Horn/Schunck: Combining Local and Global Optic Flow Methods. International Journal of Computer Vision, 2005, vol. 61, no. 3, pp. 211–231.
  10. Horn B.K.P., Schunck B.G. Determining optical flow. Artificial intelligence, 1981, vol. 17, no. 11, pp. 185–203.
  11. Kotina E.D. Beam Dynamics Formation in Magnetic Field. Proceedings of EPAC 2002, Paris, France, 2002, pp. 1264–1266.
  12. Kotina E.D. Discrete optimization problem in beam dynamics. Nuclear Instruments and Methods in Physics Research. Section A. Accelerators, Spectrometers, Detectors and Associated Equipment, 2006, vol. 558, no. 1, pp. 292–294.
  13. Kotina E.D., Leonova E.B., Ploskikh V.A. Displacement Field Construction Based on a Discrete Model in Image Processing Problems.The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 39, pp. 3–16. https://doi.org/10.26516/1997-7670.2022.39.3
  14. Kotina E.D., Ovsyannikov D.A. Velocity field based method for data processing in radionuclide studies. Problems of Atomic Science and Technology, 2018, vol. 115, no. 3, pp. 128–131.
  15. Kotina E., Ovsyannikov D., Elizarova M. Optimization approach to the velocity field determining problem. Cybernetics and physics, 2022, vol. 11, no. 3, pp. 131–135.
  16. Kotina E.D., Pasechnaya G.A. Optical flow-based approach for the contour detection in radionuclide images processing. Cybernetics and physics, 2014, vol. 3, no. 2, pp. 62–65.
  17. Kotina E., Ploskikh V., Shirokolobov A. Digital Image Processing in Nuclear Medicine. Physics of Particles and Nuclei, 2022, vol. 53, no. 2. pp. 535–540.
  18. Kopenkov V., Myasnikov V. The estimation of the traffic flow parameters based on the videoregistration data analysis. Computer Optics, 2014, vol. 38, no. 1, pp. 81–86.
  19. Ovsyannikov D. A., Kotina E. D. Determination of velocity field by given density distribution of charged particles. Problems of Atomic Science and Technology, 2012, vol. 79, no. 3, pp. 122–125.
  20. Ovsyannikov D. A., Kotina E. D., Shirokolobov A. Yu. Mathematical Methods of Motion Correction in Radionuclide Studies. Problems of Atomic Science and Technology, 2013, vol. 88, no. 6, pp. 137–140.
  21. Papenberg N., Bruhn A., Brox T. et al. Highly Accurate Optic Flow Computation with Theoretically Justified Warping. International Journal of Computer Vision, 2006, vol. 67, no. 2, pp. 141–158.

Full text (russian)