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Optimal Control Under Uncertainty and Bayesian Parameters Adjustments

Baradel, Nicolas; Bouchard, Bruno; Dang, Ngoc Minh (2018), Optimal Control Under Uncertainty and Bayesian Parameters Adjustments, SIAM Journal on Control and Optimization, 56, 2, p. 1038-1057. 10.1137/16M1070815

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01590606
Date
2018
Journal name
SIAM Journal on Control and Optimization
Volume
56
Number
2
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
1038-1057
Publication identifier
Metadata
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Author(s)
Baradel, Nicolas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Centre de Recherche en Économie et Statistique [CREST]
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dang, Ngoc Minh
Abstract (EN)
We propose a general framework for studying the 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 equation seems to be new in this context. The main difficulty lies in the nature of the set of controls which depends in a nontrivial way on the initial data through the filtration itself.
Subjects / Keywords
optimal control; uncertainty; Bayesian filtering