On the Bellman equation for some unbounded control problems

Nonlinear Differential Equations and Applications

Volumn 4, Issue 4, 1997, Pages 491-510

  Bardi, Martino ^a   Da Lio, Francesca ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011074435     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050027     Document Type: Article

References (29)

1. [BCD] M. BARDI, I. CAPUZZO DOLCETTA, Optimal control and viscosity solution of Hamilton-Jacobi-Bellman equations, Birkhäuser Verlag, Basel 1997.
2. [Ba1] G. BARLES, An approach of deterministic control problems with unbounded data, Ann. Inst. H. Poincarè, Anal. Nonlin. 7, 235-258 (1990).
3. [Ba2] G. BARLES, Uniqueness and regularity results for first order HamiltonJacobi Bellman equations, Indiana Univ. Math. J. 39, 235-258 (1990).
4. [Ba3] G. BARLES, Solutions de viscosité des équations de Hamilton-Jacobi, Springer-Verlag, Paris 1994.
5. [Ben] A. BENSOUSSAN, Pertubations methods in optimal control, John Wiley & Sons, New York 1988.
6. [CDP1] P. CANNARSA, G. DA PRATO, Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton-Jacobi equations, SIAM J. Control. Optim. 27, 861-875 (1989).
7. [CDP2] P. CANNARSA, G. DA PRATO, Some results on nonlinear optimal control problems and Hamilton-Jacobi equation in infinite dimensions, J. Funct. Anal. 90, 27-47 (1990).
8. [CS] P. CANNARSA, H.M. SONER, On the singularity of the viscosity solutions of Hamilton-Jacobi-Bellman equations, Indiana Univ. Math. J. 36, 507-524 (1987).
9. [CDL] I. CAPUZZO DOLCETTA, P.L. LIONS eds., Viscosity solutions and applications, Lecture Notes in Mathematics, Springer-Verlag, to appear.
10. [CEL] M.G. CRANDALL, L.C. EVANS, P.L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations Trans. Amer. Math. Soc. 282, 487-502 (1984).
11. [CIL1] M.G. CRANDALL, H. ISHII, P.L. LIONS, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan 39, 581-586 (1987).
12. [CIL2] M.G. CRANDALL, H. ISHII, P.L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27, 1-67 (1992).
13. [CL1] M.G. CRANDALL, P.L. LIONS, On existence and uniqueness of solutions of Hamilton-Jacobi equations, Nonlinear Anal. 10, 353-370 (1986).
14. [CL2] M.G. CRANDALL, P.L. LIONS, Remarks on the existence and uniqueness of unbounded solutions of Hamilton-Jacobi equations, Illinois J. Math. 31, 665-687 (1987).
15. [DL] F. DA LIO, On the Bellman equation for infinite horizon problems with unbounded cost functional, preprint.
16. [FS] W.H. FLEMING, H.M. SONER, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York 1992.
17. [I1] H. ISHII, Uniqueness of unbounded solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33, 721-748 (1984).
18. H. ISHII, Existence and uniqueness of solutions of Hamilton-Jacobi equations, Funktial Ekvac. 29, 167-188 (1986).
19. H. ISHII, On representations of solutions of Hamilton-Jacobi equations with convex Hamiltonians, "Recent topics in nonlineart PDE, II", 15-22, North Holland Math. Stud. 128, North Holland, Amsterdam, New York, 1985.
20. H. ISHII, Representations of solutions of Hamilton-Jacobi equations, Nonlinear Anal. 12, 121-146 (1988).
21. [L] P.L. LIONS, Generalized solutions of Hamilton-Jacobi equations, Pitman, 1982.
22. [LS] P.L. LIONS, P.E. SOUGANIDIS, Differential games, optimal control and directional derivates of viscosity solutions of Bellman's and Isaacs' equations, SIAM J. Control Optim. 23, 56G-583 (1985).
23. [ME] W.M. McENEANEY, Uniqueness for viscosity solutions of non stationary HJB equations under some a priori conditions (with applications), SIAM. J. Control Optim. 33, 1560-1576 (1995).
24. [MR1] M. MOTTA, F. RAMPAZZO, The value function of a slow growth control problem with state constraints, J. Math Systems Estimation Control, to appear.
25. 1 bounds on the controls, preprint 3, Dipartimento di Matematica, Università di Padova, 1996.
26. [R] F. RAMPAZZO, Differential Games with unbounded versus bounded controls, preprint 30, Dipartimento di Matematica, Università di Padova, 1995.
27. [S] E.D. SONTAG, Mathematical control theory: deterministic finite dimensional systems, Springer-Verlag, New York 1990.
28. ∞ control of nonlinear systems: differential games and viscosity solutions, SIAM J. Control Optim. 34 (1996).
29. [Sor2] P. SORAVIA, Optimality principle and representations formulas for viscosity solutions of Hamilton-Jacobi equations, I and II, Advances Diff. Eq., to appear.