Abstract
We introduce a class of generalized controls called random relaxed controls, and show that under quite general conditions, a partially observed, controlled diffusion will have an optimal random relaxed control whose cost equals the infimum over the costs of all ordinary controls. We also show that the optimal admissible control can be approximated arbitrarily well by very simple, ordinary controls. The proofs are based on a close analysis of the standard parts of nonstandard controls.
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Cutland, N.J., LindstrØm, T. Random relaxed controls and partially observed stochastic systems. Acta Appl Math 32, 157–182 (1993). https://doi.org/10.1007/BF00998151
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DOI: https://doi.org/10.1007/BF00998151