Open Access
Volume 27, 2021
Article Number 91
Number of page(s) 29
Published online 20 September 2021
  1. A. Altarovici, O. Bokanowski and H. Zidani, A general Hamilton-Jacobi framework for non-linear state-constrained control problems. ESAIM: COCV 19 (2013) 337–357. [CrossRef] [EDP Sciences] [Google Scholar]
  2. J-P. Aubin and A. Cellina, Differential inclusions. Set-valued maps and viability theory. Vol. 264 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo (1984). [CrossRef] [Google Scholar]
  3. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems and Control: Foundations and Applications. Birkhäuser, Boston (1997). [Google Scholar]
  4. L.D. Berkovitz, Optimal control theory. Springer, New York (1974). [Google Scholar]
  5. P. Bettiol, H. Frankowska and R.B. Vinter, Improved sensitivity relations in state constrained optimal control. Appl. Math. Optim. 71 (2015) 353–377. [Google Scholar]
  6. A. Briani and F. Rampazzo, A density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians. Nonlinear Differ. Equ. Appl. 12 (2005) 71–91. [Google Scholar]
  7. A. Briani and H. Zidani, Characterisation of the value function of final state constrained control problems with BV trajectories. Commun. Pure Appl. Anal. 10 (2011) 1567–1587. [Google Scholar]
  8. F.H. Clarke, Functional Analysis, Calculus of Variations and Optimal Control. Springer (2013). [Google Scholar]
  9. F.H. Clarke and R.B. Vinter, The relationship between the maximum principle and dynamic programming. SIAM J. Control Optim. 25 (1987) 1291–1311. [Google Scholar]
  10. F.H. Clarke and R.B. Vinter, Applications of optimal multiprocesses. SIAM J. Control Optim. 27 (1989) 1048–1071. [Google Scholar]
  11. F.H. Clarke and R.B. Vinter, Optimal multiprocesses. SIAM J. Control Optim. 27 (1989) 1072–1091. [Google Scholar]
  12. A.V. Dmitruk and A.M. Kaganovich, Maximum principle for optimal control problems with intermediate constraints. Comput. Math. Model. 22 (2011) 180–215. Translation of Nelineĭnaya Din. Upr. No. 6 (2008), 101–136. [Google Scholar]
  13. W.H. Fleming and R.W. Rischel, Deterministic and stochastic optimal control. Springer, New York (1975). [Google Scholar]
  14. H. Frankowska and M. Mazzola, On relations of the adjoint state to the value function for optimal control problems with state constraints. Nonlinear Differ. Equ. Appl. NoDEA 20 (2013) 361–383. [Google Scholar]
  15. H. Frankowska and R.B. Vinter, Existence of neighboring feasible trajectories: applications to dynamic programming for state-constrained optimal control problems. J. Optim. Theory Appl. 104 (2000) 20–40. [Google Scholar]
  16. C. Hermosilla, R.B. Vinter and H. Zidani, Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints. Systems Control Lett. 109 (2017) 30–36. [Google Scholar]
  17. C. Hermosilla, P. Wolenski and H. Zidani, The Mayer and minimum time problems with Stratied state constraints. Set-Valued Variat. Anal. 26 (2018) 643–662. [CrossRef] [Google Scholar]
  18. C. Hermosilla and H. Zidani, Infinite horizon problems on stratifiable state-constraints sets. J. Differ. Equ. 258 (2015) 1420–1460. [Google Scholar]
  19. H. Ishii, Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations. Indiana Univ. Math. J. 33 (1984) 721–748. [Google Scholar]
  20. H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Bull. Fac. Sci. Engng. Chuo Univ. 28 (1985) 3–77. [Google Scholar]
  21. P.L. Lions and B. Perthame, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians. Nonlinear Anal. Theory Methods Appl. 11 (1987) 613–621. [Google Scholar]
  22. L.S. Pontryagin, V.G. Boltjanskii, R.V. Gramkrelidze and E.F. Mishchenko, Optimal control theory. Springer, New York (1974). [Google Scholar]
  23. H. Soner, Optimal control with state-space constraint I. SIAM J. Control Optim. 24 (1986) 552–561. [Google Scholar]
  24. R.B. Vinter, New results on the relationship between dynamic programming and the maximum principle. Math. Control Signals Syst. 1 (1988) 97–105. [Google Scholar]
  25. R.B. Vinter, Optimal control. Birkhaüser, Boston (2000). [Google Scholar]
  26. X.Y. Zhou, Maximum principle, dynamic programming, and their connection in deterministic control. J. Optim. Theory Appl. 65 (1990) 363–373. [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.