Asymptotic minimization method of the integral quadratic functional on the trajectories of a quasilinear dynamical system
https://doi.org/10.29235/1561-8323-2018-62-5-519-524
Abstract
The problem of minimizing the integral quadratic functional on the trajectories of a quasilinear dynamical system with linear terminal constraints is under consideration. Asymptotic approximations to the optimal open-loop and optimal feedback controls for this problem are constructed.
Communicated by Corresponding Member Valentine V. Gorokhovik
About the Authors
A. I. Kalinin
Belarusian State University
Belarus
Belarus
Kalinin Anatoliy Iosiphovich – D. Sc. (Physics and Mathe matics), Professor.
4, Nezavisimosti Ave., 220030, Minsk
L. I. Lavrinovich
Belarusian State University
Belarus
Belarus
Lavrinovich Leonid Ivanovich – Ph. D. (Physics and Mathematics), Associate Professor.
4, Nezavisimosti Ave., 220030, Minsk
References
1. Krasovskii N. N. Theory of Control of Motion. Moscow, Nauka Publ., 1968. 476 p. (in Russian).
2. Kiselev Yu. N. An asymptotic solution of the problem of time-optimal control systems which are close to linear ones. Doklady Akademii Nauk SSSR, 1968, vol. 182, no. 1, pp. 31-34 (in Russian).
3. Falb P L., Jong J. L. Some Successive Approximation Methods on Control and Oscillation Theory. New York, London, Academic Press, 1969. 355 p. https://doi.org/10.1016/s0076-5392(08)x6152-1
4. Chernous’ko F. L., Akulenko L. D., Sokolov B. N. Control of Oscillations. Moscow, Nauka Publ., 1980. 384 p. (in Russian).
5. Kalinin A. I. Asymptotics of the Solutions of Perturbed Optimal Control Problems. Journal of Computer and Systems Sciences International, 1995, vol. 33, no. 6, pp. 75-84.
6. Gabasov R., Kirillova F. M. Qualitative theory of optimal processes. Moscow, Nauka Publ., 1971. (in Russian).
7. Mordukhovich B. Sh. Existence of optimal Controls. Sovremennye Problemy Matematiki [Modern problems of mathematics]. Moscow, VINITI, 1976, vol. 6, pp. 207-271 (in Russian).
8. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The Mathematical Theory of Optimal Processes. Moscow, New York, Gordon and Breach, 1986. 392 p.
9. Kalinin A. I. Asymptotic Methods for Optimization of Disturbed Dynamical Systems. Minsk, Ekoperspektiva Publ., 2000. 183 p. (in Russian).
10. Kalinin A. I., Lavrinovich L. I. Application of the perturbation method for the minimization of an integral quadratic functional on the trajectories of a quasilinear system. Journal of Computer and Systems Sciences International, 2014, vol. 53, no. 2, pp. 149-158. https://doi.org/10.1134/s1064230714020117
Review
Views: 1017
Email this article 