Controllability linear systems with many delays in control by the differential regulators

  • Georgii P. Razmyslovich Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Valerii V. Krakhotko Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Abstract

In the theory of controllability dynamical systems in most cases the control is selected from the class of piecewise  continuous functions. But the choise of the control from other classes is interested. In the article we consider the problem  of relative controllability of linear systems with many delays in control by the help of differential (dynamical) regulator.  The criterions of controllability in terms of parameters initial system and dynamical regulator are obtained.

Author Biographies

Georgii P. Razmyslovich, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics), docent; associate professor at the department of higher mathematics, faculty of applied mathematics and computer science

Valerii V. Krakhotko, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics), docent;  associate professor at the department of optimal control methods, faculty of applied mathematics and computer science

References

  1. Gabasov RF, Kirillova FM, Krakhotko VV. Upravlyaemost’ mnogokonturnykh sistem s sosredotochennymi parametrami. Avtomatika i telemekhanika [Automation and Remote Control]. 1971;XXI(11):18–25. Russian.
  2. Krasovskii NN. K teorii upravlyaemosti i nablyudaemosti lineinykh dinamicheskikh sistem. Prikladnaya matematika i mekhanika. 1964;28(1):3–14. Russian.
  3. Gantmaher FR. Teoriya matrits [Theory of matrices]. 4th edition. Moscow: Nauka; 1988. 552 р. Russian.
  4. Ignatenko VV. Upravlyaemost’ sistem neitral’nogo tipa so mnogimi vkhodami gruppoi obyknovennykh dinamicheskikh regulyatorov. Izvestiya AN BSSR. Seriya fiziko­matematicheskikh nauk. 1976;3:24 –33. Russian.
  5. Krakhotko VV, Razmyslovich GP. Upravlyaemost’ lineinykh sistem s zapazdyvaniem po upravleniyu pri pomoshchi dinamicheskogo regulyatora. In: Eruginskie chteniya – 2018. Tezisy dokdadov XVIII Mezhdunarodnoi nauchnoi konferentsii po differentsial’nym uravneniyam; 15–18 maya 2018 g.; Grodno, Belarus’. Chast’ 1 [Erugin reading – 2018. Abstracts of the XVIII International scientific conference on differential equations; 2018 May 15–18; Grodno, Belarus. Part 1]. Minsk: Institut matematiki NAN Belarusi; 2018. p. 120 –121. Russian.
  6. Krakhotko VV, Razmyslovich GP. Upravlyaemost’ lineinykh sistem so mnogimi zapazdyvaniyami po upravleniyu pri pomoshchi dinamicheskogo regulyatora. In: Dinamicheskie sistemy: ustoichivost’, upravlenie, optimizatsiya (DSSCO’18). Materialy Mezhdunarodnoi nauchnoi konferentsii k 100­letiyu so dnya rozhdeniya akademika E. A. Barbashina; 24 –29 sentyabrya 2018 g.; Minsk, Belarus’ [Dynamical Systems: stability, control, optimization. Proceedings of the International scientific conference to the 100th anniversary of Ye. A. Barbashin; 2018 September 24 –29; Minsk, Belarus]. Minsk: BSU; 2018. p. 143–145. Russian.
Published
2019-01-19
Keywords: controllability, observability, linear systems, systems with delay in control, dynamical regulator
How to Cite
Razmyslovich, G. P., & Krakhotko, V. V. (2019). Controllability linear systems with many delays in control by the differential regulators. Journal of the Belarusian State University. Mathematics and Informatics, 3, 82-85. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/1016