30
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Stochastic continuous control of partially observed systems via impulse control problems

&
Pages 101-127 | Received 09 Jun 1987, Published online: 04 Apr 2007

References

  • Beneš , V. and Karatzas , I. 1984 . Filtering of diffusions controlled through their conditional measures . Stochastics , 13 : 1 – 23 .
  • Bensoussan , A. 1986 . Current results and issues in stochastic control, Lecture Notes in Cont. and Inf. Sciences , Vol. 78 , 36 – 85 . Springer-Verlag .
  • Bensoussan , A. 1983 . Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions . Stochastics , 9 : 169 – 222 .
  • Bensoussan , A. and Lions , J,-L . 1982 . Contrô impulsionnel et inéquations quasUvariationelles , Paris : Dunod .
  • Bensoussan , A. and Runggaldier , W. J, . 1986 . A method for constructing ∈-optimal controls in problems with partial observation of the state, Lecture Notes in Cont. and Inf. Sciences , 89 – 99 . Springer-Verlag .
  • Bismut , J.-M . 1979 . Un problème de controle stochastique avec observation partielle . Z, Wahr. verw. Gebiete , 49 : 63 – 95 .
  • Borkar , V. S. 1983 . Existence of optimal controls for partially observed diffusions . Stochastic , 11 ( 1,2 ) : 103 – 142 .
  • Christopeit , N. 1980 . Existence of optimal stochastic controls under partial observation . Z. Wahr, verw. Gebiete , 51 ( 1,2 ) : 201 – 213 .
  • Christopeit , N. and Helmes , K. 1983 . Separation principle for partially observed linear control problems, Lecture Notes in Cont. and Inf. Sciences , Vol. 61 , 36 – 60 . Springer-Verlag .
  • Cohen , R. 1986 . On a solution to the control of partially observed linear systems with non-quadratic cost, Lecture Notes on Control and Information Sciences , Vol. 78 , 127 – 137 . Springer-Verlag .
  • Cohen , R. 1987 . Modélisation, filtrage et contrôle de processus stochastiques, Thése de Doctorat de 1'ENST Vol. 87 ,
  • Davis , M. H. A. 1979 . Martingale methods in stochastic control, Lecture Notes in Cont. and Inf. Sciences , Vol. 16 , 86 – 117 . Springer-Verlag .
  • Davis , M. H. A. 1977 . Linear Estimation and Stochastic Control , Chapman and Hall .
  • Davis , M. H. A. 1976 . The separation principle in stochastic control via Girsanov solutions . SIAM J. Cont , 14 : 176 – 188 .
  • Davis , M. H. A. and Kohlman , M. 1981 . On the non-linear semi-group of stochastic control under partial observations, Publication No. EECON 81-10 , London : Imperial College .
  • Davis , M. H. A. and Varayia , P. 1973 . Dynamic programming conditions for partially observable systems . SIAM J. Cont , 11 : 226 – 261 .
  • Dellacherie , C. and Meyer , P. A. 1972 and 1973 . Probabilities et Potentiel , Paris : Herman .
  • Dynkin , E. B. 1965 . Markov Processes , Berlin : Springer-Verlag .
  • El Karoui , N. B. 1981 . Aspects probabilistes du contrhle stochastique, In: Ecole d'Cte de Saint-Flour MII, Lecture Notes in Mathematics , Vol. 876 , Berlin : Springer-Verlag .
  • El Karoui , N. , Huu Nguyen , D. and Piquet-Jeanblanc , M. 1965 . Existence of an optimal Markovian control under partial observation . SIAM J. Cont ,
  • El Karoui , N. , Lepeltier , J. P. and Marchal , B. Arrkt optimal dependant d'un parametre et contrhle continu Markovien, Unpublished.
  • El Karoui , N. , Lepeltier , J. P. and Marchal , B. 1982 . Semi-groupe de Nisio associe au contr8le de processus de Markov, Lecture Notes in Control and Information Sciences , Vol. 43 , Berlin : Springer-Verlag .
  • Fujisaki , M. , Kallianpur , G. and Kunita , H. 1972 . Stochastic differential equations for non-linear filtering problem . Osaka J. Math , 9 : 19 – 40 .
  • Fleming , W. H. 1982 . Non-linear semi-group for controlled partially observed diffusions . SIAM J. Cont , 20 : 286 – 301 .
  • Fleming , W. H. and Nisio , M. 1984 . On stochastic relaxed control for partially observed diffusions . Nagoya J. Math , 93 : 71 – 108 .
  • Fleming , W. H. and Pardoux , E. 1982 . Optimal control of partially observed diffusions . SIAM J. Cont , 20 : 261 – 285 .
  • Haussmann , U. G. 1982 . Optimal control of partially observed diffusions via separation principle, Lecture Notes in Control and Information Sciences , Vol. 43 , Springer-Verlag .
  • Haussmann , U. G. 1986 . Existence of optimal Markovian controls for degenerate diffusions, Lecture Notes in Control and Information Sciences , Vol. 78 , Berlin : Springer-Verlag .
  • Ikeda , N. and Watanabe , S. 1981 . Stochastic Differential Equations and Diffusion Processes , North-Holland : Amsterdam .
  • Kallianpur , G. 1980 . Stochastic Filtering Theory . Springer-Verlag ,
  • Korezlioglu , H. and Mazziotto , G. 1984 . Approximations of the non-linear filter by periodic sampling and quantization, 6eme Conference INRIA sur I'anayse et l'optimisation des systemes Nice
  • Krylov , N. V. 1988 . An approach to controlled diffusion processes . Theor. of Prob , 31 ( 4 ) : 604 – 626 .
  • Krylov , N. V. 1980 . Controlled Diffusion Processse , Springer-Verlag .
  • Kushner , H. J. 1977 . Probability Methods for Approximations in Stochastic Control and for Elliptic Equations , Academic Press .
  • Lepeltier , J.-P and Marchal , B. 1984 . Théorie générate du contrôle impulsionnel Markovian . SIAM J. Cont , 22 : 645 – 665 .
  • Liptser , R. S. and Shiryayev , A. N. 1977 . Statistics of Random Processes, Applications of Math , Vol. 15 , Springer-Verlag .
  • Mazziotto , G. Approximate impulse of partially observed systems . Proceed, of the Conf. on Modelling and Filtering . Rome.
  • Mazziotto , G. and Szpirglas , J. 1983 . Separation principle for impulse control in partial information . Stochastics , 10 : 47 – 73 .
  • Mazziotto , G. , Stettner , L. , Szpirglas , J. and Zabzyck , J. 1988 . On impulse control with partial observation . SIAM J Control and Optimization , 26 : 967 – 984 .
  • Menaldi , J.-L . 1980 . On the optimal impulse control problem for degenerate diffusions . SIAM J. Cont , 18 : 722 – 739 .
  • Menaldi , J.-L and Robin , M. 1983 . On some cheap control problems for diffusion processes . Trans. Am. Math. Soc , 18
  • Menaldi , J. L. and Rofman , E. 1982 . On stochastic control problems with impulse cost vanishing, Lecture Notes in Economics and Mathematical Systems , Vol. 215 , Berlin : Springer-Verlag .
  • Nagai , H. 1980 . On an impulsive control of additive processes . Z. Wahr V. Geb , 53 : 1 – 16 .
  • Nisio , M. 1976 . On stochastic optimal controls and envelope of Markovian semi-groups . Inter. Symp. SDE Kyoto , 53 : 297 – 325 .
  • Robin , M. 1978 . ContrBle impulsionnel des processus de Markov , Vol. IX , Thèse Université Paris .
  • Veretennikov , A. J. 1981 . On strong solutions and explicit formulas for stochastic integral equations . Math. USSR Sbornik , 39 : 387 – 403 .
  • Wonham , W. H. 1968 . On the separation theorem of stochastic control . SIAM J. Cont , 6 : 312 – 326 .
  • Zakai , M. 1969 . On the optimal filtering of diffusion processes . Z. Wahr. V. Geb , 11 : 230 – 249 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.