- PII
- 10.31857/S0374064123120105-1
- DOI
- 10.31857/S0374064123120105
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 59 / Issue number 12
- Pages
- 1702-1709
- Abstract
- Sufficient conditions for the existence of optimal trajectories in general optimal control problems with free terminal time as well as in sub-Lorentzian problems are obtained.
- Keywords
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 12
References
- 1. Wald R.M. General Relativity. Chicago, 1984.
- 2. Beem J.K., Ehrlich P.E., Easley K.L. Global Lorentzian Geometry. Monographs Textbooks Pure Appl. Math. V. 202. New York; Basel; Hong Kong, 1996.
- 3. M"uller O., S\'anchez M. An Invitation to Lorentzian Geometry // Jahresber. Deutsch. Math. Ver. 2014. V. 115. P. 153-183.
- 4. Montgomery R. A Tour of Subriemannnian Geometries, their Geodesics and Applications. Providence, 2002.
- 5. Agrachev A., Barilari D., Boscain U. A Comprehensive Introduction to sub-Riemannian Geometry from Hamiltonian Viewpoint. Cambridge, 2019.
- 6. Grochowski M. Reachable sets for the Heisenberg sub-Lorentzian structure on $\mathbb{R}^3.$ An estimate for the distance function // J. of Dynamical and Control Systems. 2006. V. 12. № 2. P. 145-160.
- 7. Grochowski M. Geodesics in the sub-Lorentzian geometry // Bull. Polish. Acad. Sci. Math. 2002. V. 50. P. 161-178.
- 8. Grochowski M. Normal forms of germs of contact sub-Lorentzian structures on $\mathbb{R}^3.$ Differentiability of the sub-Lorentzian distance // J. Dynam. Control Systems. 2003. V. 9. № 4. P. 531-547.
- 9. Grochowski M. Properties of reachable sets in the sub-Lorentzian geometry // J. Geom. Phys. 2009. V. 59. № 7. P. 885-900.
- 10. Grochowski M. Reachable sets for contact sub-Lorentzian metrics on $\mathbb{R}^3.$ Application to control affine systems with the scalar input // J. Math. Sci. 2011. V. 177. № 3. P. 383-394.
- 11. Grochowski M. On the Heisenberg sub-Lorentzian metric on $\mathbb{R}^3$ // Geometric Singularity Theory. Banach Center Publications. Warszawa, 2004. V. 65. P. 57-65.
- 12. Chang D.-C., Markina I., Vasil'ev A. Sub-Lorentzian geometry on anti-de Sitter space // J. Math. Pures Appl. 2008. V. 90. P. 82-110.
- 13. Korolko A., Markina I. Nonholonomic Lorentzian geometry on some H-type groups // J. Geom. Anal. 2009. V. 19. P. 864-889.
- 14. Grong E., Vasil'ev A. Sub-Riemannian and sub-Lorentzian geometry on $SU(1, 1)$ and on its universal cover // J. Geom. Mech. 2011. V. 3. № 2. P. 225-260.
- 15. Grochowski M., Medvedev A., Warhurst B. 3-dimensional left-invariant sub-Lorentzian contact structures // Differ. Geometry and its Appl. 2016. V. 49. P. 142-166.
- 16. Jurdjevic V. Geometric Control Theory. Cambridge, 1997.
- 17. Аграчев А.А., Сачков Ю.Л. Геометрическая теория управления. M., 2005.
- 18. Сачков Ю.Л. Введение в геометрическую теорию управления. М., 2021.
- 19. Сачков Ю.Л. Лоренцева геометрия на плоскости Лобачевского // Мат. заметки. 2023. V. 114. № 1. P. 127-130.
- 20. Bonnard B., Jurdjevic V., Kupka I., Sallet G. Transitivity of families of invariant vector fields on the semidirect products of Lie groups // Trans. Amer. Math. Soc. 1982. V. 271. № 2. P. 525-535.
