Asymptotic method for solving the problem of transition process optimization in a three-tempo singularly perturbed system
https://doi.org/10.29235/1561-8323-2024-68-3-183-187
Abstract
The problem of constructing a transition process with minimal energy costs for a linear singularly perturbed system containing three groups of variables with significantly different rates of change is considered. Asymptotic approximations to solving this problem are constructed in the form of an open-loop and feedback controls. The main advantage of the proposed computational procedures is that the original problem is split into three unperturbed optimal control problems of lower dimension.
About the Authors
A. I. Kalinin
Belarusian State University
Belarus
Belarus
Kalinin Anatoly I. – D. Sc. (Physics and Mathematics), Professor
4, Nezavisimosti Ave., 220030, Minsk
L. I. Lavrinovich
Belarusian State University
Belarus
Belarus
Lavrinovich Leonid I. – Ph. D. (Physics and Mathematics), Associate Professor
4, Nezavisimosti Ave., 220030, Minsk
References
1. Dmitriev M. G., Kurina G. A. Singular perturbations in control problems. Automation and Remote Control, 2006, vol. 67, no. 1, pp. 1–43. https://doi.org/10.1134/s0005117906010012
2. Kalinin A. I. The Asymptotics of the Solution of Perturbed Optimal Control Problems. International Journal of Computer and Systems Sciences, 1995, vol. 33, pp. 75–84.
3. Zhang Y., Naidu D. S., Cai C., Zou Y. Singular perturbation and time scales in control theories and applications. An overview 2002–2012. International Journal of Information and Systems Sciences, 2014, vol. 9, no. 1, pp. 1–36.
4. Kokotovic P. V., Khalil H. K. Singular perturbations in systems and control. New York, 1986.
5. Kurina G. A., Kalashnikova M. A. Singularly Perturbed Problems with Multi-Tempo Fast Variables. Automation and Remote Control, 2022, vol. 83, no. 11, pp. 1679–1723. https://doi.org/10.1134/s00051179220110017
6. Krasovskii N. N. Theory of control of motion: linear systems. Moscow, 1968. 476 p. (in Russian).
7. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The mathematical theory of optimal processes. 4th ed. Moscow, 1983. 392 p. (in Russian).
8. Vasil’eva A. B. Asymptotic methods in the theory of ordinary differential equations containing small parameters in front of the higher derivatives. USSR Computational Mathematics and Mathematical Physics, 1963, vol. 3, no. 4, pp. 823–863. https://doi.org/10.1016/0041-5553(63)90381-1
Review
Views: 251
Email this article 