Free access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 415 - 441
DOI http://dx.doi.org/10.1051/cocv:2001116
Published online 15 August 2002
  1. O. Alvarez, Bounded-from-below solutions of Hamilton-Jacobi equations. Differential Integral Equations 10 (1997) 419-436. [MathSciNet]
  2. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston (1997).
  3. M. Bardi and F. Da Lio, On the Bellman equation for some unbounded control problems. NODEA Nonlinear Differential Equations Appl. 4 (1997) 276-285.
  4. M. Bardi, M. Falcone and P. Soravia, Numerical methods for pursuit-evasion games and viscosity solutions, in Stochastic and Differential Games: Theory and Numerical Methods, edited by M. Bardi, T.E.S. Raghavan and T. Parthasarathy. Birkhäuser, Boston (1999).
  5. M. Bardi and P. Soravia, Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games. Trans. Amer. Math. Soc. 325 (1991) 205-229. [CrossRef] [MathSciNet]
  6. C. Castaing, Sur les multi-applications mesurables. RAIRO Oper. Res. 1 (1967).
  7. M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67. [CrossRef] [MathSciNet]
  8. F. Da Lio, On the Bellman equation for infinite horizon problems with unbounded cost functional. Appl. Math. Optim. 41 (1999) 171-197. [CrossRef] [MathSciNet]
  9. W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer, New York (1993).
  10. G.B. Folland, Real Analysis: Modern Techniques and their Applications. J. Wiley and Sons, New York (1984).
  11. H. Ishii, On representation of solutions of Hamilton-Jacobi equations with convex Hamiltonians, in Recent Topics in Nonlinear PDE II, edited by K. Masuda and M. Mimura. Kinokuniya Company, Tokyo (1985).
  12. V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997).
  13. M. Malisoff, A remark on the Bellman equation for optimal control problems with exit times and noncoercing dynamics, in Proc. 38th IEEE Conf. on Decision and Control. Phoenix, AZ (1999) 877-881.
  14. M. Malisoff, Viscosity solutions of the Bellman equation for exit time optimal control problems with vanishing Lagrangians (submitted).
  15. P. Soravia, Pursuit-evasion problems and viscosity solutions of Isaacs equations. SIAM J. Control. Optim. 31 (1993) 604-623. [CrossRef] [MathSciNet]
  16. P. Soravia, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians. Comm. Partial Differential Equations 18 (1993) 1493-1514. [CrossRef] [MathSciNet]
  17. P. Soravia, Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations I: Equations of unbounded and degenerate control problems without uniqueness. Adv. Differential Equations 4 (1999) 275-296. [MathSciNet]
  18. P. Soravia, Optimal control with discontinuous running cost: Eikonal equation and shape from shading, in Proc. 39th IEEE CDC (to appear).
  19. P. Souganidis, Two-player, zero-sum differential games and viscosity solutions, in Stochastic and Differential Games: Theory and Numerical Methods, edited by M. Bardi, T.E.S. Raghavan and T. Parthasarathy. Birkhäuser, Boston (1999).
  20. H.J. Sussmann, A general theorem on local controllability. SIAM J. Control Optim. 25 (1987) 158-194. [CrossRef] [MathSciNet]
  21. H. Sussmann, From the Brachystochrone problem to the maximum principle, in Proc. of the 35th IEEE Conference on Decision and Control. IEEE Publications, New York (1996) 1588-1594.
  22. H.J. Sussmann, Geometry and optimal control, in Mathematical Control Theory, edited by J. Baillieul and J.C. Willems. Springer-Verlag, New York (1998) 140-198.
  23. H.J. Sussmann and B. Piccoli, Regular synthesis and sufficient conditions for optimality. SISSA Preprint 68/96/M. SIAM J. Control Optim. (to appear).
  24. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972).
  25. M.I. Zelikin and V.F. Borisov, Theory of Chattering Control. Birkhäuser, Boston (1994).