On the existence of stochastic optimal control of distributed state system

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 4, 2003, Pages 1153-1184

  Buckdahn, Rainer ^a   Raşcanu, Aurel ^b  

^a UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^b ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Adjoint variable; Ekeland's principle; Optimal control; Parabolic stochastic differential equations; Skorohod theorem; Tightness

Indexed keywords

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; DIFFUSION; SET THEORY; STATE SPACE METHODS; STOCHASTIC CONTROL SYSTEMS;

PARABOLIC STOCHASTIC DIFFERENTIAL EQUATIONS;

OPTIMAL CONTROL SYSTEMS;

EID: 0037290471     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00158-X     Document Type: Article

References (28)

1. Barbu V., Iannelli M. Optimal control of population dynamics. J. Optim. Theory Appl. 102(1):1999;1-14.
2. Barbu V., Seidman T. Existence for a minimization problem in Banach spaces. J. Math. Anal. Appl. 121:1987;96-108.
3. Bensoussan A. Stochastic maximum principle for distributed parameter systems. J. Franklin Inst. 315:1983;387-406.
4. A. Bensoussan, Some existence results for stochastic partial differential equations, Da Prato, G. (ed.) et al., Stochastic partial differential equations and applications. Proceedings of the third meeting on stochastic partial differential equations and applications held at Villa Madruzzo, Trento, Italy, January 1990. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 268 (1992) 37-53.
5. Bensoussan A., Raşcanu A. Stochastic variational inequalities in infinite dimensional spaces. Numer. Func. Anal. Optim. 18(1&2):1997;19-54.
6. Bismut J. On optimal control of linear stochastic equations with a linear-quadratic criterion. SIAM J. Control Optim. 15(1):1977;1-4.
7. Cannarsa P., Da prato G. Second order Hamilton-Jacobi equations in infinite dimensions. SIAM J. Control Optim. 29(2):1991;474-492.
8. Cerrai S. Hamilton-Jacobi equation for reaction-diffusion control systems. SIAM Control Optim. 39(6):2001;1779-1816.
9. Da prato G., Kwapien S., Zabczyk J. Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics. 23:1987;1-23.
10. Da prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge University Press, Cambridge.
11. G. Da prato, J. Zabczyk, Differentiability of the Feynman-Kac semigroup and a control application, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Nat., Rend. Lincei (9) Mat. Appl. 8(3) (1997) 183-188.
12. Ekeland I. On the variational principle. J. Math. Anal. Appl. 47:1974;324-353.
13. El Karoui N., Huu Nguyen D., Jeanblanc-Pique M. Compactification methods in the control of degenerate diffusions. Stochastics. 20:1987;169-219.
14. M. Fuhrman, G. Tessitore, Infinite horizon optimal stochastic control in Hilbert spaces via backward stochastic equations, preprint, 2001.
15. Gatarek D., Sobczyk J. On the existence of optimal controls of Hilbert space-valued diffusions. SIAM J. Control Optim. 32(1):1994;170-175.
16. Gozzi F. Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem. Commun. Partial Differential Equations. 20(5&6):1995;775-826.
17. Hu Y., S Peng Maximum principle for semilinear stochastic evolution control systems. Stochastics Stochastics Rep. 33(3-4):1990;159-180.
18. Nagase N. On the existence of optimal control for controlled stochastic partial differential equations. Nagoya Math. J. 115:1989;73-85.
19. Nagase N., Nisio M. Optimal controls for stochastic partial differential equations. SIAM J. Control Optim. 28(1):1990;186-213.
20. Nisio M. Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations. Nagoya Math. J. 123:1991;13-37.
21. M. Nisio, On sensitive control for stochastic partial differential equations, in: H. Kunita et al. (ed.), Stochastic Analysis on Infinite Dimensional Spaces, Proceedings of the U.S.-Japan Bilateral Seminar, January 4-8, 1994, Baton Rouge, LA, USA, Pitman Research Notes Mathematical Series, Vol. 310, Longman Scientific and Technical, Essex, Harlow, 1994, pp. 231-241.
22. M. Nisio, Game approach to risk sensitive control for stochastic evolution systems, in: W.M. McEneaney, et al. (Eds.), Stochastic Analysis, Control, Optimization and Applications, A volume in Honor of Wendell H. Fleming, on the Occasion of his 70th Birthday, Birkhauser, Boston, 1999, pp. 115-134.
23. E. Pardoux, Equations aux dérivées partielles stochastiques nonlinéaires monotones, Etude de solutions fortes du type Itô, Thèse, Paris-Sud, Orsay, 1975.
24. Pardoux E., Peng S. Backward SDE's and quasilinear PDE's, stochastic PDE and their applications. Rozovski B.L., Sowers R.B. Lecture Notes in Computer Science. Vol. 176:1992;Springer, Berlin.
25. Pardoux E., Rascanu A. Backward stochastic differential equations with subdifferential operators and related variational inequalities. Stochastic Process. Appl. 76(2):1998;191-215.
26. Pardoux E., Rascanu A. Backward stochastic variational inequalities. Stochastics Stochastics Rep. 67(3-4):1999;159-167.
27. Peng S. Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 27:1993;125-144.
28. Rong S., Chan W.L. Existence of solutions and optimal control for reflecting stochastic differential equations with applications to population control theory. Stochastic Anal. Appl. 10(1):1992;45-106.