An estimation from within of the reachable set of nonlinear R. Brockett integrator with small nonlinearity
DOI:
https://doi.org/10.2298/YJOR121005026MKeywords:
control problem, reachable set, R. Brockett integrator, estimation from withinAbstract
In this paper, the nonlinear R. Brockett integrator with small nonlinear addition to the right-hand side of the corresponding differential equations is considered. More precisely, investigating the possibility to estimate from within the corresponding reachable set, we have obtained an efficient form of the ellipsoidal estimation from within. We used our previous results on the similar theme.References
Kavski, M., "Chronological algebras", Results of Science and Technology, Contemporary Mathematics and its applications, Thematic reviews, 60 VINITI, Moscow, 1999, 144–178.
Brockett, R.W., "Asymptotic stability and feedback stabilization", Differential Geometric Control Theory, Proceedings of Conference of the Michigan Technological University, 1982, 181–191.
Nikolskii, M. S., "About an estimate of reachable set of R. Brockett nonlinear integrator", Differential Equations, 36, (11) 2000, 1501–1505. (in Russian)
Lee, E.B. and Markus, L., "Foundations of the Optimal Control Theory", John Wiley & Sons, New York, 1970. (in Russian)
Ioffe, A.D., and Tikhomirov, V.M., "Theory of extremal problems", Nauka, Moscow., 1974. (in Russian)
Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V., "Optimal Control", Nauka, Moscow, 1979. (in Russian)
Hartman, Ph., "Ordinary Differential Equations", John Wiley & Sons, New York, 1964. (in Russian)
Blagodatskikh V.I., and Filippov, A.F., "Differential Inclusions and Optimal Control", Proceedings of Steklov Mathematical Institute of the USSR Academy of Sciences, 169 (1985) 194–252. (in Russian)
Downloads
Published
Issue
Section
License
Copyright (c) 2013 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.