Geodesic
Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. Part 1
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 1, pp. 73-84
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Many different works are devoted to the problems of control and optimization in dynamic systems. Interest in these tasks does not decrease with time. New challenges arise in the development of technological processes in various fields of science and technology, in particular, in the design and creation of modern electrophysical equipment. In this paper, the problem of optimization and control of trajectory beams is considered. The problem of joint optimization of the program motion and the beam of perturbed motions using a combination of smooth and nonsmooth functionals is investigated. The first part deals with the mathematical formulation of the given representation of the variation of investigated functional and provides optimality conditions in the form of a maximum principle. In the second part, the problem of optimization of dynamics of charged particles in the accelerator with spatially homogeneous quadrupole focusing will be considered. Using a combination of smooth and non-smooth functions allows you to set the functionals that most accurately reflect the requirements for the dynamics of the charged particle beam in accelerators.
Keywords: optimal control, controlled dynamic system, trajectory ensemble, smooth functional, non-smooth functional, maximum principle, charged particle beam, accelerator. 
@article{VSPUI_2020_16_1_a6,
     author = {D. A. Ovsyannikov and M. A. Mizintseva and M. Yu. Balabanov and A. P. Durkin and N. S. Edamenko and E. D. Kotina and A. D. Ovsyannikov},
     title = {Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. {Part~1}},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {73--84},
     year = {2020},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_1_a6/}
}
TY  - JOUR
AU  - D. A. Ovsyannikov
AU  - M. A. Mizintseva
AU  - M. Yu. Balabanov
AU  - A. P. Durkin
AU  - N. S. Edamenko
AU  - E. D. Kotina
AU  - A. D. Ovsyannikov
TI  - Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. Part 1
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 73
EP  - 84
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2020_16_1_a6/
LA  - ru
ID  - VSPUI_2020_16_1_a6
ER  - 
%0 Journal Article
%A D. A. Ovsyannikov
%A M. A. Mizintseva
%A M. Yu. Balabanov
%A A. P. Durkin
%A N. S. Edamenko
%A E. D. Kotina
%A A. D. Ovsyannikov
%T Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. Part 1
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2020
%P 73-84
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2020_16_1_a6/
%G ru
%F VSPUI_2020_16_1_a6
D. A. Ovsyannikov; M. A. Mizintseva; M. Yu. Balabanov; A. P. Durkin; N. S. Edamenko; E. D. Kotina; A. D. Ovsyannikov. Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. Part 1. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 1, pp. 73-84. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_1_a6/

[1] A. B. Kurzhansky, Control in case of uncertainty, Fizmatlit, M., 1977, 394 pp. (In Russian)

[2] D. A. Ovsyannikov, Mathematical methods of beam control, Leningrad State University Publ., L., 1980, 228 pp. (In Russian)

[3] D. A. Ovsyannikov, Modeling and optimization of charged particle beam dynamics, Leningrad State University Publ., L., 1990, 312 pp. (In Russian)

[4] T. F. Ananyna, “The problem of control in case of partial data”, Differential Equations, 13:4 (1976), 612–620 (In Russian) | MR

[5] A. Panteleev, V. V. Semenov, Synthesis of optimal control systems with incomplete information, Moscow Aviation Institute Publ. House, M., 1992, 191 pp. (In Russian)

[6] A. S. Bortakovsky, “Optimal and suboptimal control of beams of trajectories of deterministic continuous-discrete systems”, Proceedings of the Russian Academy of Sciences. Theory and control systems, 2009, no. 1, 18–33 (In Russian) | MR | Zbl

[7] A. B. Kurzhanski, P. Varaiya, “Dynamic optimization for reachability problems”, Journal of Optimization Theory and Applications, 108 (2001), 227–251 | DOI | MR | Zbl

[8] E. D. Kotina, “Discrete optimization problem in beam dynamics”, Nucl. Instrum. Methods Phys. Res. A, 558:1 (2006), 292–294 | DOI

[9] V. V. Altsybeyev, D. A. Ovsyannikov, “Optimization of beam parameters in APF channel”, 27th International Linear Accelerator Conference LINAC 2014 (Geneva, 2014), 722–725

[10] D. A. Ovsyannikov, “Mathematical methods of optimization of charged partical beams dynamics”, Proceeding of the European Partical Accelerator Conference (Barselona, Spain, 1996), v. 2, 1382–1384 | MR

[11] B. Bondarev, A. Durkin, A. Ovsyannikov, “New mathematical optimization models for RFQ structures”, Proceedings of the Particle Accelerator Conference (New York City, 1999), v. 4, 2808–2810

[12] T. K. Vinogradova, V. F. Demyanov, “On the minimax principle in optimal control problems”, Reports of the USSR Academy of Sciences, 213:3 (1973), 512–514 (In Russian) | Zbl

[13] V. F. Demyanov, T. K. Vinogradova, V. N. Nikulina et al., Non-Smooth problems of optimization and control theory, Leningrad University Publ., L., 1982, 324 pp. (In Russian) | MR

[14] A. D. Ovsyannikov, “On a class of optimization problems in electrostatic field”, Reports of the Academy of Sciences, 453:4 (2013), 383–385 (In Russian) | Zbl

[15] A. D. Ovsyannikov, “Control of the program and perturbed movements”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2006, no. 4, 111–124 (In Russian)

[16] A. D. Ovsyannikov, “Beam control of charged particles taking into account their interaction”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2009, no. 2, 82–92 (In Russian)

[17] A. D. Ovsyannikov, Mathematical models of beam dynamics optimization, Publishing House “BBM”, Saint Petersburg, 2014, 181 pp. (In Russian)

[18] D. A. Ovsyannikov, V. V. Altsybeyev, “On the beam dynamics optimization problem for an alternating-phase focusing linac”, Phys. Part. Nuclei Lett., 13:7 (2016), 775–779 | DOI

[19] D. A. Ovsyannikov, A. D. Ovsyannikov, M. F. Vorogushin, Yu. A. Svistunov, A. P. Durkin, “Beam dynamics optimization: models, methods and applications”, Nucl. Instrum. Methods Phys. Res. A, 558:1 (2006), 11–19 | DOI | MR

[20] A. D. Ovsyannikov, A. P. Durkin, D. A. Ovsyannikov, Y. A. Svistunov, “Acceleration of different ion types in single RFQ structure”, Problems of Atomic Science and Technology, 3(103) (2016), 54–56

[21] D. A. Ovsyannikov, N. S. Edamenko, “Modeling of charged particle beam dynamics”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2013, no. 2, 60–65 (In Russian)

[22] A. D. Ovsyannikov, D. A. Ovsyannikov, V. V. Altsybeyev, A. P. Durkin, V. G. Papkovich, “Application of optimization techniques for RFQ design”, Problems of Atomic Science and Technology, 3(91) (2014), 116–119

[23] A. D. Ovsyannikov, D. A. Ovsyannikov, S. L. Chung, “Optimization of a radial matching section”, International Journal of Modern Physics A, 24:5 (2009), 952–958 | DOI

[24] A. D. Ovsyannikov, D. A. Ovsyannikov, S. L. Chung, “Optimization of matching section of an accelerator with a spatially uniform quadrupole focusing”, Technical Physics. The Russian Journal of Appl. Phys., 11 (2009), 1663–1666

[25] D. A. Ovsyannikov, A. D. Ovsyannikov, I. Antropov, V. Kozynchenko, “BDO-RFQ code and optimization models”, Proceedings of the International Conference of Physics and Control, 2005, 282–288

[26] D. A. Ovsyannikov, M. A. Mizintseva, A. D. Ovsyannikov, “Joint optimization of smooth and nonsmooth functionals on beams of trajectories”, Optimal control and differential games, Proceedings of the International Conference dedicated to the 110th anniversary of the birth of Lev Semenovich Pontryagin, Steklov Mathematical Institute of RAS, M., 2018, 203–205 | MR

[27] M. Yu. Balabanov, M. A. Mizintseva, D. A. Ovsyannikov, “Beam dynamics optimization in a linear accelerator”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 14:1 (2018), 4–13 | MR

[28] M. A. Mizintseva, “On one problem of minimization of smooth and non-smooth functionals”, Vestnik of Saint Petersburg State University of Technology and Design. Series 1. Natural and Technical Sciences, 2018, no. 2, 37–41 (In Russian)

[29] M. Mizintseva, D. Ovsyannikov, “Minimax problem of simultaneous optimization of smooth and non-smooth functionals”, Constructive non-smooth analysis and related topics, Proceedings of the Conference CNSA 2017, IEEE, 2017, 218–222

[30] M. Mizintseva, D. Ovsyannikov, “On the minimax problem of beam dynamics optimization”, 25th Russian Particle Accelerator Conference, RuPAC 2016 (Saint Petersburg, 2016), 360–362

[31] L. S. Pontryagin, V. G. Boltyansky, R. V. Gamkrelidze, E. F. Mishchenko, Mathematical theory of optimal processes, Nauka, M., 1969, 384 pp. (In Russian) | MR

[32] I. M. Kapchinsky, Theory of linear resonance accelerators, Energoizdat, M., 1982, 239 pp. (In Russian)

[33] A. Golovkina, D. Ovsyannikov, S. Olaru, “Performance optimization of radioactive waste transmutation in accelerator driven system”, Cybernetics and Physics, 7:4 (2018), 210–215 | DOI

[34] D. Ovsyannikov, S. Zavadskiy, “Pareto-optimal choice of controlled dimension for plasma stabilization system”, IFAC-Papers OnLine, 51:32 (2018), 175–178 | DOI

[35] P. Bazhanov, E. Kotina, D. Ovsyannikov, V. Ploskikh, “Optimization algorithm of the velocity field determining in image processing”, Cybernetics and Physics, 7:4 (2018), 174–181 | DOI