Quantum-Mechanical Model of the Relay and Pulse Control Dynamics

The main purpose of the article was to consider the conceptual model of the dynamics of inertial objects relay and pulse control. The model possesses the properties of quantum mechanical systems. We confirm the validity of the proposed model by the numerical experiment. The results obtained reveal new characteristics of relay and pulse systems and provide the key to the synthesis of the more advanced control algorithms.

References

[1] Raushenbakh B.V., Tokar’ E.N. Upravlenie orientatsiey kosmicheskikh apparatov [Spacecraft Attitude Control]. Moscow, Nauka Publ., 1976. 600 p.

[2] Gaushus E.V. Issledovanie dinamicheskikh sistem metodom tochechnykh preobrazovaniy [Study of dynamic systems by the point transformation method]. Moscow, Nauka Publ., 1976. 368 p.

[3] Simonyants R.P. Quantum and synergistic properties of dynamical relay systems. Aerokosmicheskie tekhnologii, 2004-2007. Tr. Vseross. i Mezhdunar. nauch.-tekh. konf. [Aerospace technologies, 2004-2007. Proc. All-Russian and Int. Sci. Tech. Conf.]. Reutov-Moscow, 2004-2007. Moscow, NPO mashinostroeniya, MGTU im. N.E. Baumana Publ., 2008, pp. 168-182 (in Russ.).

[4] Pitaevskiy L.P. Macroscopic quantum phenomena. Sov. Phys. Usp., 1967, vol. 9, pp. 888-891. DOI: 10.1070/PU1967v009n06ABEH003230

[5] Kornienko N.E. About development of nonlinear-quantum macrophysics and nonlinear-wave model of energy channels of alive organisms (About a nature of the chines meridianes). Fizika zhivogo [Physics of the Alive], 2008, vol. 16, no. 1, pp. 5-22 (in Russ.).

[6] Gushchina O.A. Quantum model of motivational process. Vestnik VUiT [Vestnik of Volzhsky Univ. after V.N. Tapishchev], 2011, no. 22, pp. 7-10 (in Russ.).

[7] Lerner S. Information Path Functional and Informational Macro Dynamics. N.Y., Nova Sc. Publ., 2010.

[8] Ponomarenko V.P. Fluctuations, bifurcation and chaos in a system with frequen-cy-phase control. Tr. XII Vseross. soveshchaniya po problemam upravleniya [Proc. of the XII All-Russia Meeting on Control Problems]. Moscow, 2014, June 16-19. Moscow, Institut problem upravleniya im. V.A. Trapeznikova RAN Publ., 2014, pp. 295-307 (in Russ.). Available at: http://vspu2014.ipu.ru/prcdngs (accessed 10.05.2015).

[9] Galaev A.A., Ignat’ev A.A. Nonlinear feedback-based control of the distribution of total energy between the degrees of freedom of a mechanical system. A quantum approach. Automation and Remote Control, 2008, vol. 69, no. 3, pp. 363-373. DOI: 10.1134/S000511790803003X

[10] Simonyants R.P., Budyka S.M. A computer model for nonlinear dynamics of spacecraft attitude control. Tr. vseros. nauch. tekhn. konf. "Aerokosmicheskie tekhnologii" [Proc. All-Russian Sci. Tech. Conf. "Aerospace technology"]. Moscow, Bauman Moscow State Tech. Univ, 2003, pp. 197-203 (in Russ.).

[11] Shil’nikov L.P., Shil’nikov A.L., Turaev D.V., Chua L. Metody kachestvennoy teorii v nelineynoy dinamike. Ch. 2. [Methods of Qualitative Theory in Nonlinear Dynamics]. Moscow, Izhevsk, NITs "Regulyarnaya i khaoticheskaya dinamika", Institut komp’yuternykh issledovaniy Publ. [SRC "Regular and Chaotic Dynamics", Institute of Computer Science], 2009. 548 p.

[12] Landau L.D., Lifshitz E.M. Quantum Mechanics. Non-Relativistic Theory (Course of Theoretical Physics. Vol. 3). Pergamon Press, 1965. 616 p.

[13] Baykov Yu.A., Kuznetsov V.M. Kvantovaya mekhanika [Quantum Mechanics]. Moscow, BINOM. Laboratoriya znaniy Publ., 2013. 291 p.