Abstract
A stochastic control problem whose dynamics are only partially observed is solved. In earlier literature it was conjectured that for such problems an optimal relaxed control exists. In this article we prove that for the problem under consideration the optimal relaxed control exists and is the weak limit of a minimizing sequence of ordinary controls. Making use of the special discrete nature of the observations and of the special form of the drift function the existence of an optimal ordinary control is derived.
The general partially observed control problem is then approximated by a sequence of problems of the above form, i.e., with discrete observations. In this way the existence of an ordinary optimal control is derived for the general problem.
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Communicated by A. V. Balakrishnan
During part of his work on this topic the author was a guest of the SFB 72 of the Deutsche Forschungsgemeinschaft of the University of Bonn.
The author's work was partially supported by the Deutsche Forschungsgemeinschaft within the SFB 72 of the University of Bonn.
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Elliott, R.J., Kohlmann, M. On the existence of optimal partially observed controls. Appl Math Optim 9, 41–66 (1982). https://doi.org/10.1007/BF01460117
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DOI: https://doi.org/10.1007/BF01460117