Solution of the local boundary problem for nonlinear stationary system with account of the computer systems verification

Authors

  • Aleksandr N. Kvitko St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Nikolay N. Litvinov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2024.204

Abstract

In the article an algorithm of construction of the control function that garantees the translation of nonlinear stationary system of the ordinary differential equations from initial state to origin of the coordinate system with account of the possibility of the onboard computer systems verification is suggested. A constructive sufficient conditions that garafntee an existence of the problem solution are found. An efficiency of the algorithm is shown by numerical modelling of the specific practical problem.

Keywords:

control, nonlinear stationary systems, boundary problem, stabilization, computer systems

Downloads

Download data is not yet available.
 

References

Литература

1. Зубов В. И. Лекции по теории управления. Москва, Наука (1975).

2. Крищенко А. П. Исследование управляемости и множеств достижимости нелинейных систем управления. Автоматика и техника 6, 30-36 (1984).

3. Coron, J.-M. Control and Nonlinearity. Mathematical Surveys and Monographs 136. AMS, Providence (2007).

4. Kvitko A. N., Maksina A. M. Chistyakov S. V. On a method for solving a local boundary problem for a nonlinear stationary system with perturbations in the class of piecewise constant controls. Int. J. Robust Nonlinear Control 29, 4515-4536 (2019).

5. Aeyels D. Controllability for polynomial systems. Lect. Notes Contr. and Inf. Sci. 63, 542-545 (1984).

6. Qin H. On the controllability of nonlinear control system. Comput. & Maths. with Appls. 10 (6), 441-451 (1985).

7. КрасовскийН. Н. Теория управления движением. Москва, Наука (1968).

8. Кабанов С. А. Оптимизация параметров систем с коррекциейпараметров структуры управления. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 1 (59), вып. 2, 254-260 (2014).

9. Квитко А. Н., Фирюлина О. С., Еремин А. С. Алгоритм решения краевойзадачи для нелинейной системы и его численное моделирование. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 4 (4), 608-621 (2017). https://doi.org/10.21638/11701/spbu01.2017.409

10. Квитко А. Н., Литвинов Н. Н. Решение локальнойграничнойзадачи в классе дискретных управленийдля нелинейнойнестационарнойсистемы. Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления 18, вып. 1, 18-36 (2022).

11. Управление и наведение беспилотных маневренных летательных аппаратов на основе современных информационных технологий. Красильщикова М. Н., Себрякова Г. Г. (ред.). Москва, Физматлит (2003).

References

1. Zubov V. I. Lectures in control theory. Moscow, Nauka Publ. (1975). (In Russian)

2. Krishchenko A. P. Controllability and Attainability Sets of Nonlinear Control Systems. Avtomatika i tekhnika Автоматика и техника 6, 30-36 (1984). (In Russian) [Eng. transl.: Autom. Remote Control. 45 (6). Part 1, 707-713 (1984)].

3. Coron J.-M. Control and Nonlinearity. Mathematical Surveys and Monographs 136. AMS, Providence (2007).

4. Kvitko A. N., Maksina A. M. Chistyakov S. V. On a method for solving a local boundary problem for a nonlinear stationary system with perturbations in the class of piecewise constant controls. Int. J. Robust Nonlinear Control 29, 4515-4536 (2019).

5. Aeyels D. Controllability for polynomial systems. Lect. Notes Contr. and Inf. Sci. 63, 542-545 (1984).

6. Qin H. On the controllability of nonlinear control system. Comput. & Maths. with Appls. 10 (6), 441-451 (1985).

7. Krasovskii N. N. Theory of control of motion. Moscow, Nauka Publ. (1968). (In Russian)

8. Kabanov S. A. Dynamic system optimization using correction of control structure parameters. Vestnik of Saint-Petersburg University. Mathematics. Mechanics. Astronomy 1 (59), iss. 2, 254-260 (2014). (In Russian)

9. Kvitko A. N., Firyulina O. S., Eremin A. S. An algorithm of solution of a boundary value problem for a nonlinear stationary control system it modelling. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (4), 608-621 (2017). https://doi.org/10.21638/11701/spbu01.2017.409 (In Russian) [Eng. transl.: Vestnik St. Petersburg University. Mathematics 4 (62), iss. 4, 608-621 (2017) https://doi.org/10.21638/11701/spbu01.2017.409].

10. Kvitko A. N., Litvinov N. N. Solution of a local boundary problem for a non-linear non-stationary system in the class of discrete controls. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Sciences. Control Processes 18, iss. 1, 18-36 (2022). (In Russian)

11. Control and guidance of unmanned maneuverable aircraft based on modern information technologies. Krasilshchikov M. N., Sebryakov G. G. (eds). Moscow, Fizmatlit Publ. (2003). (In Russian)

Downloads

Published

2024-08-10

How to Cite

Kvitko, A. N., & Litvinov, N. N. (2024). Solution of the local boundary problem for nonlinear stationary system with account of the computer systems verification. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(2), 303–315. https://doi.org/10.21638/spbu01.2024.204

Issue

Vol. 11 No. 2 (2024)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.