Abstract
The optimal control of a nonlinear partially observed stochastic control system is computed through using nonlinear filtering and linear quadratic techniques.
This work was partially supported by NSF grant DMS-9105649.
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V.E. Beneš, I. Karatzas, “On the Relation of Zakai's and Mortensen's Equation”, SIAM J. Control and Optimization 21 (1983) 472–489.
A. Bensoussan, “Optimal Control of Partially Observed Diffusions”, in “Advances in Filtering and Optimal Stochastic Control”, W.H. Fleming, L.A. Gorostiza (Eds.), Proceedings of the IFIP-WG 7/1 Working Conference, Springer Lecture Notes in Control and Information Sciences, Vol. 42 (1982).
N. Christopeit, M. Kohlmann (Eds.), “Stochastic Differential Systems”, Proceedings of the 2nd Bad Honnef Conference, Springer Lecture Notes in Control and Information Sciences, vol. 43 (1982).
W.H. Fleming, “Nonlinear Semigroups for Controlled Partially Observed Diffusions”, SIAM Journal on Control and Optimization, Vol. 20, (1982).
K. Helmes, R.W. Rishel, “The Solution of a Partially Observed Stochastic Control Problem in Terms of Predicted Miss”, to appear.
R.S. Lipster, A.N. Shiryayev, Statistics of Random Processes I-General Theory, Springer-Verlag (1977).
H. Kunita, “Asymptotic Behavior of the Nonlinear Filtering Errors of Markov Processes” Journal of Multivariate Analysis 1 (1971), pp. 365–391.
H.J. Kushner, “On the Dynamical Equations of Conditional Probability Density Functions with Application to Optimal Stochastic Control Theory”, J. Math. Anal. Appl. 8 (1964), pp. 332–344.
R.E. Mortensen, “Stochastic Optimal Control with Noisy Observations”, International J. Control 4 (1966), pp. 455–464.
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© 1992 Springer-Verlag
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Helmes, K.L., Rishel, R.W. (1992). An optimal control depending on the conditional density of the unobserved state. In: Karatzas, I., Ocone, D. (eds) Applied Stochastic Analysis. Lecture Notes in Control and Information Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007054
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DOI: https://doi.org/10.1007/BFb0007054
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