Free Access
Volume 22, Number 3, July-September 2016
Page(s) 786 - 810
Published online 18 May 2016
  1. A.A. Agrachev and Yu. L. Sachkov, Control Theory from the Geometric Viewpoint. Springer-Verlag (2004). [Google Scholar]
  2. A. Agrachev, G. Stefani and P. Zezza, An invariant second variation in optimal control. Int. J. Control 71 (1998) 689–715. [Google Scholar]
  3. M.S. Aronna, J.F. Bonnans, A.V. Dmitruk and P. Lotito, Quadratic order conditions for bang-singular extremals. AIMS J. Numer. Algebra Control Optim. 2 (2012) 511–546. [CrossRef] [Google Scholar]
  4. A. Bacciotti and G. Stefani, On the relationship between global and local controllability. Math. Syst. Theory 16 (1983) 79–91. [CrossRef] [Google Scholar]
  5. R.M. Bianchini, Good needle-like variations. In vol. 64 of Proceedings of Symposia in Pure Mathematics (1999). [Google Scholar]
  6. R.M. Bianchini, Variational cones and high-order maximum principles. Technical report, Dipartimento di Matematica “Ulisse Dini”, viale Morgagni 67/a, Firenze (1994). [Google Scholar]
  7. R.M. Bianchini, Variational Approach to Some Optimization Control Problems. In Geometry in Nonlinear Control and Differential Inclusions. Edited by G. Ferreyra R. Gardner H. Hermes and H. Sussmann (1995). [Google Scholar]
  8. R.M. Bianchini and G. Stefani, A High Order Maximum Principle, in Analysis and Control of Linear Systems. Edited by R.E. Saeks C.I. Byrnes, C.F. Martin (1988). [Google Scholar]
  9. A. Bressan and F. Rampazzo, Impulsive control systems with commutative vector fields. J. Optim. Theory Appl. 71 (1991) 67–84. [CrossRef] [Google Scholar]
  10. A. Bressan and F Rampazzo, Impulsive control systems without commutativity assumptions. J. Optim. Theory Appl. 81 (1994) 435–457. [CrossRef] [Google Scholar]
  11. F.C. Chittaro and G. Stefani, Singular extremals in multi-input time-optimal problem: a sufficient condition. Control Cyber. 39 (2010). [Google Scholar]
  12. F.C. Chittaro and G. Stefani, Minimum-Time Strong Optimality of a Singular Arc: extended Dubins Problem. In 52nd IEEE Conference on Decision and Control (2013). [Google Scholar]
  13. B.D. Craven, Control and Optimization. Chapman & Hall Mathematics Series. Chapman & Hall, London, New York (1995). [Google Scholar]
  14. A. V. Dmitruk. Quadratic condition for a weak minimum for singular regimes in optimal control problems. Soviet Math Dokl. 18 (1977). [Google Scholar]
  15. A. V. Dmitruk, Jacobi type conditions for singular extremals. Control Cybernet. 37 (2008) 285–306. [MathSciNet] [Google Scholar]
  16. R. Gabasov and F.M. Kirillova, High order necessary conditions for optimality. SIAM J. Control 10 (1972) 127–168. [CrossRef] [MathSciNet] [Google Scholar]
  17. B. S. Goh, The second variation for singular Bolza problems. SIAM J. Control Optim. 4 (1966) 309–325. [CrossRef] [Google Scholar]
  18. M. Guerra and A. Sarychev, Fréchet generalized trajectories and minimizers for variational problems of low coercivity. J. Dyn. Contr. Syst. 21 (2015) 351–377. [CrossRef] [Google Scholar]
  19. M.R. Hestenes, Application of the theory of quadratic forms in Hilbert spaces to the calculus of variations. Pac. J. Math. 1 (1951) 525–581. [Google Scholar]
  20. V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997). [Google Scholar]
  21. V. Jurdjevic and F. Monroy-Pérez, Variational Problems on Lie Groups and Their Homogeneous Spaces: Elastic Curves, Tops, and Constrained Geodesic Problems (2002). [Google Scholar]
  22. A.J. Krener, A generalization of Chow’s theorem and the bang-bang theorem to nonlinear control problems. SIAM J. Control Optim. 12 (1974) 43–52. [CrossRef] [Google Scholar]
  23. J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Texts Appl. Math. Springer (1999). [Google Scholar]
  24. E.J. McShane, Unified Integration. Academic Press (1983). [Google Scholar]
  25. L. Poggiolini and G. Stefani, Bang-singular-bang extremals: sufficient optimality conditions. J. Dyn. Control Syst. 17 (2011) 469–514. [Google Scholar]
  26. G. Stefani, Minimum-time optimality of a singular arc: second order sufficient conditions. In vol. 1 of 43rd IEEE Conference on Decision and Control (2004). [Google Scholar]
  27. G. Stefani, Strong Optimality of Singular Trajectories. Geometric Control and nonsmooth analysis. Edited by F. Ancona A. Bressan P. Cannarsa F. Clarke and P. R. Wolenski (2008). [Google Scholar]
  28. G. Stefani and P. Zezza. Constrained regular LQ-control problems. SIAM J. Control Optim. 35 (1997) 876–900. [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.