Existence of Sub-Lorentzian Longest Curves

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

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.

Sobre autores

Yu. Sachkov

Program Systems Institute, Russian Academy of Sciences

Autor responsável pela correspondência
Email: yusachkov@gmail.com
Pereslavl-Zalessky, Yaroslavl oblast, 152020 Russia

Bibliografia

  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.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar

Declaração de direitos autorais © Russian Academy of Sciences, 2023