Control Time in Systems of Chaotic Behavior. II. Its Estimation
- 26 Downloads
The control time of dynamic systems is estimated by a method based on the properties of a sequence of reachable sets. It is shown to depend on the rate of growth of the volume of reachable sets. The method for studying controllability is applicable to systems with chaotic behavior of trajectories. For control systems generated by neutral mappings, an asymptotic estimate for the control time is found under arbitrarily small controls.
KeywordsDynamic System Control System Mechanical Engineer System Theory Chaotic Behavior
Unable to display preview. Download preview PDF.
- 1.Khryashchev, S.M., Control Time in Systems of Chaotic Behavior. I, Avtom. Telemekh., 2004, no. 10, pp. 51–67.Google Scholar
- 2.Khryashchev, S.M., Estimation of Transport Times for Chaotic Dynamical Control Systems, Proc. Int. Conf. Physics and Control, Russia, 2003, pp. 528–533.Google Scholar
- 3.Katok, A.B. and Khasselblat, B., Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem(Introduction to Modern Theory of Dynamic Systems), Moscow: Faktorial, 1999.Google Scholar
- 4.Osipenko, G.S., The Symbolic Image of a Dynamic System, Tr. Konf. Granichnye Zadachi (Proc. Conf. oundary Problems), Perm, Russia, 1983.Google Scholar
- 5.Osipenko, G.S. and Khryashchev, S.M., Controllability and Applied Symbolic Dynamics, Proc. 13th Int. Symp. Math. Theory of Networks and Systems, Padova, Italy, 1998, pp. 349–352.Google Scholar
- 6.Khryashchev, S.M., O Lokal'noi upravlyaemosti dinamicheskoi sistemy vdol' traektorii (Local Controlla-bility of a Dynamic System along Trajectories), Available from VINITI, 1997, St. Petersburg, no. 868-V.Google Scholar
- 7.Agrachev, A.A., Vakhrameev, S.A., and Gamkrelidze, R.V., Differential Geometric and Group-Theoretic Methods in Control Theory, in Sb. Problemy geometrii (A Collection of Geometric Problems), Moscow: VINITI, 1983, vol. 14, pp. 3–56.Google Scholar