Identyfikatory
Warianty tytułu
Problemy ekstremalne dla systemów hiperbolicznych z warunkami brzegowymi, w których występują całkowe opóźnienia czasowe
Języki publikacji
Abstrakty
Extremal problems for integral time lag hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which integral time lags appear in the Neumann boundary conditions are solved. Such systems constitute, in a linear approximation, a universal mathematical model for many processes in which transmission signals at a certain distance with electric, hydraulic and other long lines take place. The time horizon is fixed. Making use of Dubovicki-Milyutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
Zaprezentowano ekstremalne problemy dla systemów hiperbolicznych z całkowymi opóźnieniami czasowymi. Rozwiązano problem optymalnego sterowania brzegowego dla systemów hiperbolicznych drugiego rzędu, w których całkowe opóźnienia czasowe występują w warunkach brzegowych typu Neumanna. Tego rodzaju systemy stanowią w liniowym przybliżeniu uniwersalny model matematyczny procesów fizycznych, w których ma miejsce przesyłanie sygnałów na odległość w liniach długich typu elektrycznego, hydraulicznego i innych. Korzystając ze schematu Dubowickiego-Milutina wyprowadzono warunki konieczne i wystarczające optymalności dla problemu liniowo-kwadratowego.
Czasopismo
Rocznik
Tom
Strony
23--30
Opis fizyczny
Bibliogr. 18 poz., wzory
Twórcy
autor
- AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Institute of Automatic Control and Robotics, Al. Mickiewicza 30, 30-059 Cracow, Poland
Bibliografia
- 1. Gilbert E.G., An iterative procedure for computing the minimum of a quadratic form on a convex set. “SIAM Journal on Control”, Vol. 4, No. 1, 1966, 61-80, DOI: 10.1137/0304007.
- 2. Girsanov I.V., Lectures on the Mathematical Theory of Extremal Problems, Publishing House of the University of Moscow, Moscow, 1970 (in Russian).
- 3. Kowalewski A., On optimal control problem for parabolic-hyperbolic system. “Problems of Control and Information Theory”, Vol. 15, No. 5, 1986, 349-359.
- 4. Kowalewski A., Miśkowicz M., Extremal problems for time lag parabolic systems. Proceedings of the 21st International Conference of Process Control (PC), 446-451, Strbske Pleso, Slovakia, June 6-9, 2017.
- 5. Kowalewski A., Extremal Problems for Distributed Parabolic Systems with Boundary Conditions involving Time-Varying Lags. Proceedings of the 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), 447-452, Międzyzdroje, Poland, August 28-31, 2017, DOI: 10.1109/MMAR.2017.8046869.
- 6. Kowalewski A., Extremal problems for parabolic systems with time-varying lags. “Archives of Control Sciences”, Vol. 28, No. 1, 2018, 89-104, DOI: 10.24425/119078.
- 7. Kowalewski A., Extremal problems for infinite order parabolic systems with time-varying lags. Advances in Intelligent Systems Soft Computing, Vol. 1196, 2020, Springer Nature Switzerland AG, DOI: 10.1007/978-3-030-50936-1_1.
- 8. Kowalewski A., Extremal problems for parabolic systems with multiple time-varying lags. Proceedings of 23rd International Conference on Methods and Models in Automation and Robotics (MMAR), 791-796, Międzyzdroje, Poland, August 27-30, 2018, DOI: 10.1109/MMAR.2018.8485815.
- 9. Kowalewski A., Miśkowicz M., Extremal problems for integral time lag parabolic systems. Proceedings of the 24th International Conference on Methods and Models in Automation and Robotics (MMAR), 7-12, Międzyzdroje, Poland, August 26-29, 2019, DOI: 10.1109/MMAR.2019.8864638.
- 10. Kowalewski A., Duda J., On some optimal control problem for a parabolic system with boundary condition involving a time-varying lag. “IMA Journal of Mathematical Control and Information”, Vol. 9, No. 2, 1992, 131-146, DOI: 10.1093/imamci/9.2.131.
- 11. Kowalewski A., Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays. AGH University of Science and Technology Press, Cracow 2001.
- 12. Kowalewski A., Extremal problems for time lag hyperbolic systems. Proceedings of the 25th International Conference on Methods and Models in Automation and Robotics (MMAR), 245-250, Międzyzdroje, Poland, August 23-26, 2021, DOI: 10.1109/MMAR49549.2021.9528456.
- 13. Kowalewski A., Extremal problems for second order hyperbolic systems with multiple time delays. “Archives of Control Sciences”, Vol. 33, No. 1, 2023, 101-126, DOI: 10.24425/acs.2023,145116.
- 14. Kowalewski A., Extremal problems for hyperbolic systems with boundary conditions involving time-varying delays. Proceedings of the 26th International Conference on Methods and Models in Automation and Robotics (MMAR), 122-127, Międzyzdroje, Poland, August 24-25, 2022, DOI: 10.1109/MMAR55195.2022.9874285
- 15. Kowalewski A., Extremal problems for second order hyperbolic systems with boundary conditions involving multiple time-varying delays. “Pomiary Automatyka Robotyka”, R. 27, Nr 2, 2023, 69-76, DOI: 10.14313/PAR-248/69.
- 16. Lions J.L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.
- 17. Lions J.L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin, 1972.
- 18. Maslov V.P., Operators Methods, Moscow, 1973 (in Russian).
Uwagi
Adam Kowalewski was supported under the research program no. 16.16.120.773 at AGH University of Science and Technology, Cracow, Poland.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-52d24326-e000-471c-881e-545e79a69ee6
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.