Free Access
Issue
ESAIM: COCV
Volume 21, Number 4, October-December 2015
Page(s) 939 - 957
DOI https://doi.org/10.1051/cocv/2014047
Published online 20 May 2015
  1. Z. Artstein, Pontryagin Maximum Principle revisited with feedbacks. Eur. J. Control 17 (2011) 46–54. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.V. Arutyunov, Optimality Conditions. Abnormal and Degenerate Problems, 1st edition. Kluwer Academic Publishers, Dordrecht (2000). [Google Scholar]
  3. A. Arutyunov, D. Karamzin and F.L. Pereira, Maximum principle in problems with mixed constraints under weak assumptions of regularity. J. Optim. 59 (2010) 1067–1083. [CrossRef] [Google Scholar]
  4. P. Bettiol and H. Frankowska, Lipschitz regularity of solution map of control systems with multiple state constraints. Discrete Contin. Dyn. Syst. A 32 (2012) 1–26. [Google Scholar]
  5. P. Bettiol, A. Boccia and R.B. Vinter, Stratified necessary conditions for differential inclusions with state constraints. SIAM J. Control Optim. 51 (2013) 3903–3917. [CrossRef] [MathSciNet] [Google Scholar]
  6. M.H.A. Biswas and M.d.R. de Pinho, A Variant of Nonsmooth Maximum Principle for State Constrained Problems. IEEE Proc. of 51th CDC (CDC12) (2012) 7685–7690. [Google Scholar]
  7. M.H.A. Biswas, Necessary Conditions for Optimal Control Problems with State Constraints: Theory and Applications. Ph.D. thesis, University of Porto, Faculty of Engineering, DEEC, PDEEC (2013). [Google Scholar]
  8. F. Clarke, Optimization and Nonsmooth Analysis. John Wiley, New York (1993). [Google Scholar]
  9. F. Clarke, Y. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York (1998). [Google Scholar]
  10. F. Clarke, Necessary conditions in dynamic optimization. Mem. Amer. Math. Soc. (2005). [Google Scholar]
  11. F. Clarke and M.d.R. de Pinho, The Nonsmooth Maximum Principle. Control Cybern. 38 (2009) 1151–1168. [Google Scholar]
  12. F. Clarke and M.d.R. de Pinho, Optimal control problems with mixed constraints. SIAM J. Control Optim. 48 (2010) 4500–4524. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Clarke, Y. Ledyaev and M.d.R. de Pinho, An extension of the Schwarzkopf multiplier rule in optimal control. SIAM J. Control Optim. 49 (2011) 599–610. [CrossRef] [MathSciNet] [Google Scholar]
  14. M.d.R. de Pinho and R.B. Vinter, An Euler-Lagrange inclusion for optimal control problems. IEEE Trans. Automat. Control 40 (1995) 1191–1198. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.d.R. de Pinho, M.M.A. Ferreira and F.A.C.C. Fontes, An Euler-Lagrange inclusion for optimal control problems with state constraints. Dyn. Control Syst. 8 (2002) 23–45. [CrossRef] [Google Scholar]
  16. M.d.R. de Pinho, M.M.A. Ferreira and F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614–632. [CrossRef] [EDP Sciences] [Google Scholar]
  17. M.d.R. de Pinho, P. Loewen and G.N. Silva, A weak maximum principle for optimal control problems with nonsmooth mixed constraints. Set-Valued Var. Anal. 17 (2009) 203–221. [CrossRef] [MathSciNet] [Google Scholar]
  18. E.N. Devdaryani and Y.S. Ledyaev, Maximum principle for implicit control systems. Appl. Math. Optim. 40 (1999) 79–103. [CrossRef] [MathSciNet] [Google Scholar]
  19. A.V. Dmitruk, Maximum principle for the general optimal control problem with phase and regular mixed constraints. Comput. Math. Model. 4 (1993) 364–377. [CrossRef] [MathSciNet] [Google Scholar]
  20. M.R. Hestenes, Calculus of Variations and Optimal Control Theory. John Wiley, New York (1966). [Google Scholar]
  21. M.M.A. Ferreira, F.A.C.C. Fontes and R.B. Vinter, Nondegenerate necessary conditions for nonconvex optimal control problems with state constraints. J. Math. Anal. Appl. 233 (1999) 116–129. [CrossRef] [MathSciNet] [Google Scholar]
  22. F.A.C.C. Fontes and S.O. Lopes, Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints. J. Math. Anal. Appl. 399 (2013) 27–37. [CrossRef] [MathSciNet] [Google Scholar]
  23. H. Frankowska, Regularity of minimizers and of adjoint states for optimal control problems under state constraints. J. Convex Anal. 13 (2006) 299–328. [Google Scholar]
  24. I. Kornienko and M.d.R. de Pinho, Differential inclusion approach for mixed constrained problems revisited. Prepublished in: Set Valued Var. Anal. (2014) DOI:10.1007/s11228-014-0315-2. [Google Scholar]
  25. I. Kornienko and M.d.R. de Pinho, Properties of some control systems with mixed constraints in the form of inequalities. Report, ISR, DEEC, FEUP (2013). Available at http://paginas.fe.up.pt/˜mrpinho/ [Google Scholar]
  26. B. Mordukhovich, Variational analysis and generalized differentiation. Basic Theory. Fundamental Principles of Mathematical Sciences 330. Springer-Verlag, Berlin (2006). [Google Scholar]
  27. H.J. Pesch and M. Plail, The Maximum Principle of optimal control: A history of ingenious ideas and missed opportunities. Control Cybern. 38 (2009) 973–995. [Google Scholar]
  28. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mischenko, The Mathematical Theory of Optimal Processes. John Wiley, New York (1962). [Google Scholar]
  29. R.T. Rockafellar and B. Wets, Variational Analysis. Vol. 317 of Grundlehren Math. Wiss. Springer-Verlag, Berlin (1998). [Google Scholar]
  30. R.B. Vinter and G. Pappas, A maximum principle for nonsmooth optimal-control problems with state constraints. J. Math. Anal. Appl. 89 (1982) 212–232. [CrossRef] [MathSciNet] [Google Scholar]
  31. R.B. Vinter, Optimal Control. Birkhäuser, Boston (2000). [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.