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Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain

De Cooman, Gert; Troffaes, Matthias C.M.

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Authors

Gert De Cooman



Abstract

We generalise the optimisation technique of dynamic programming for discrete-time systems with an uncertain gain function. We assume that uncertainty about the gain function is described by an imprecise probability model, which generalises the well-known Bayesian, or precise, models. We compare various optimality criteria that can be associated with such a model, and which coincide in the precise case: maximality, robust optimality and maximinity. We show that (only) for the first two an optimal feedback can be constructed by solving a Bellman-like equation.

Citation

De Cooman, G., & Troffaes, M. C. (2005). Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 39(2-3), 257-278. https://doi.org/10.1016/j.ijar.2004.10.004

Journal Article Type Article
Publication Date 2005-06
Deposit Date Feb 29, 2008
Publicly Available Date May 14, 2009
Journal International Journal of Approximate Reasoning
Print ISSN 0888-613X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 39
Issue 2-3
Pages 257-278
DOI https://doi.org/10.1016/j.ijar.2004.10.004
Keywords Optimal control, Dynamic programming, Uncertainty, Imprecise probabilities, Lower previsions, Sets of probabilities.

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