# Optimal Control Under Uncertainty and Bayesian Parameters Adjustments

@article{Baradel2016OptimalCU, title={Optimal Control Under Uncertainty and Bayesian Parameters Adjustments}, author={Nicolas Baradel and Bruno Bouchard and Ngoc-Minh Dang}, journal={SIAM J. Control. Optim.}, year={2016}, volume={56}, pages={1038-1057} }

We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayesian rule after each impulse. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. The derivation of the dynamic programming…

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