Optimization of a linear dynamic system with periodic changing parameters

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

Abstract

The article deals with the problem of optimal control of a linear dynamic system with periodic parameters. The qualitative theory of such problems is developed very fully if the period of coefficients of the system is not very small. With a small period, there are serious difficulties with integration. Therefore, it is reasonable to supplement the constructive methods of solution with asymptotic ones. The article presents such an approach that the method of averaging is used to construct an auxiliary (basic) problem, estimates of the proximity of solutions to the initial and basic problems are obtained.

Author Biographies

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

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

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

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

Vladimir V. Goryachkin, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

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

References

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Published
2020-03-31
Keywords: linear systems, optimal control, systems with small parameters, asymptotic methods
How to Cite
Krakhotko, V. V., Razmyslovich, G. P., & Goryachkin, V. V. (2020). Optimization of a linear dynamic system with periodic changing parameters. Journal of the Belarusian State University. Mathematics and Informatics, 1, 75-79. https://doi.org/10.33581/2520-6508-2020-1-75-79