Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1554047