Open Access
Volume 29, 2023
Article Number 17
Number of page(s) 31
Published online 27 February 2023
  1. A.A. Agrachev, A. Morse, E.D. Sontag, H.J. Sussmann and V.I. Utkin, Nonlinear and Optimal Control Theory, Cetraro, Italy (2004), n. 1932, Springer, xiv+351. [Google Scholar]
  2. F. Angrisani and F. Rampazzo, Quasi Differential Quotients. Preprint arXiv:2107.07638 (2021). [Google Scholar]
  3. M.S. Aronna, M. Motta and Rampazzo, A higher-order maximum principle for impulsive optimal control problem. SIAM J. Control Optim. 58 (2020) 814-844. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.P. Aubin and A. Cellina, Differential inclusions: set-valued maps and viability theory. Springer (1984), xiii+342. [Google Scholar]
  5. J.P. Aubin and H. Frankowska, Vol. 2 of Set-valued analysis. System, Control, Foundation and Applications. Birkhauser, Boston (1990) [Google Scholar]
  6. D. Azimov and R. Bishop, New trends in astrodynamics and applications: optimal trajectories for space guidance. Ann. N Y Acad. Sci. 1065 (2005) 189-209. [CrossRef] [PubMed] [Google Scholar]
  7. A. Bressan, Hyper-impulsive motions and controllizable coordinates for Lagrangian systems. Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 19 (1989) (1991) 195-246. [MathSciNet] [Google Scholar]
  8. A. Bressan and M. Motta, A class of mechanical systems with some coordinates as controls. A reduction of certain optimization problems for them. Solutions methods. Mem. Mat. Acc. Lincei, s. 9 2 (1993) 5-30 [Google Scholar]
  9. A. Bressan and F. Rampazzo, Moving constraints as stabilizing controls in classical mechanics. Arch. Ration. Mech. Anal. 196 (2010) 97-141. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Calcaterra, Basic properties of nonsmooth Hörmander vector fields and Poincaré’s inequality. Commun. Math. Anal. 11 (2011) 1-40. [MathSciNet] [Google Scholar]
  11. F. Cardin and C. Viterbo, Commuting Hamiltonians and Hamilton-Jacobi multi-time equations. Duke Math. J. 144 (2008) 235-284. [CrossRef] [MathSciNet] [Google Scholar]
  12. A.J. Catllá, D.G. Schaeffer. T.P. Witelski, E.E. Monson, A.L. Lin, On spiking models for synaptic activity and impulsive differential equations. SIAM Rev. 50 (2008) 553-569. [CrossRef] [MathSciNet] [Google Scholar]
  13. F.H. Clarke, Y.S. Ledyaev, R.J. Stern and R.R. Wolenski, Nonsmooth Analysis and Control Theory Graduate Texts in Mathematics, Volume 178, 1998, Springer, xiii+278. [Google Scholar]
  14. F. Clarke, Functional analysis, calculus of variations and optimal control Graduate Texts in Mathematics, 264, 2013. 264, Springer, London, xiv+591. [Google Scholar]
  15. E. Feleqi and F. Rampazzo, Iterated Lie brackets for nonsmooth vector fields. NoDEA Nonlinear Differ. Equ. Appl. 24 (2017) Paper No. 61, 1-43. [CrossRef] [Google Scholar]
  16. P.H. Gajardo, C. Ramirez and A. Rapaport, Minimaltime sequential batch reactors with bounded and impulse controls for one or more species. SIAM J. Control Optim. 47 (2008) 2827-2856. [Google Scholar]
  17. C.M. Marle, Geomátrie des systèmes mácaniques a liaisons actives. Symp. Geometry Math. Phys. (1991) 260-287. [CrossRef] [Google Scholar]
  18. A. Montanari and D. Morbidelli, Balls defined by nonsmooth vector fields and the Poincaráe inequality. Ann. Inst. Fourier (Grenoble) 54 (2004) 431-452. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Montanari and D. Morbidelli, On the subRiemannian cut locus in a model of free two-step Carnot group. Calc. Variat. Partial Differ. Equ. 56 (2017) 1-26. [CrossRef] [Google Scholar]
  20. B.S. Mordukhovich and H.J. Sussmann, Nonsmooth analysis and geometric methods in deterministic optimal control. Vol. 78 of The IMA Volumes in Mathematics and its Applications. Springer (1996), ix+246. [Google Scholar]
  21. M. Palladino and F. Rampazzo, A geometrically based criterion to avoid infimum-gaps in optimal control. J. Differ. Equ. 269 (2020) 10107-10142. [CrossRef] [Google Scholar]
  22. F. Rampazzo, On the Riemannian structure of a Lagrangian system and the problem of adding time-dependent constraints as controls. Eur. J. Mech. A Solids 10 (1991) 405-431. [Google Scholar]
  23. F. Rampazzo, Frobenius-type theorems for Lipschitz distributions. J. Differ. Equ. 243 (2007) 270-300. [CrossRef] [Google Scholar]
  24. F. Rampazzo and H.J. Sussmann, Commutators of flow maps of nonsmooth vector fields. J. Differ. Equ. 232 (2007) 134-175. [CrossRef] [Google Scholar]
  25. F. Rampazzo and H.J. Sussmann, Set-valued differentials and non-smooth version of Chow’s theorem. Proc. of the 40th IEEE Conf. on Decision and Control, Orlando, FL, December 2001, vol. 3, IEEE publications, New York (2001), pp. 111-129. [Google Scholar]
  26. S. Simic, Lipschitz distributions and Anosov flows. Proc. Am. Math. Soc. 124 (1996) 1869-1877. [CrossRef] [Google Scholar]
  27. H.J. Sussmann, High-order point variations and generalized differentials. Geometric control and nonsmooth analysis. Ser. Adv. Math. Appl. Sci., 76, World Sci. Publ., Hackensack, NJ (2008) 327-357. [Google Scholar]
  28. H.J. Sussmann, Warga derivate containers and other generalized differentials in Proceedings of the 41st IEEE Conference on Decision and Control (2002). [Google Scholar]
  29. R. Vinter, Optimal Control Modern Birkhäuser Classics. Springer (2010) xx+507. [Google Scholar]
  30. J. Warga, Controllability, extremality, and abnormality in nonsmooth optimal control. J. Optim. Theory Appl. 41 (1983) 239-260. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Warga, Optimization and controllability without differentiability assumptions. SIAM J. Control Optim. 21 (1983) 837-855. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.