Mathematics – Optimization and Control
Scientific paper
2009-07-16
Mathematics
Optimization and Control
23 pages 13 figures: This is an abridged/summarized version with explicit proofs either sketched or skipped. The full expanded
Scientific paper
Decision processes with incomplete state feedback have been traditionally modeled as Partially Observable Markov Decision Processes. In this paper, we present an alternative formulation based on probabilistic regular languages. The proposed approach generalizes the recently reported work on language measure theoretic optimal control for perfectly observable situations and shows that such a framework is far more computationally tractable to the classical alternative. In particular, we show that the infinite horizon decision problem under partial observation, modeled in the proposed framework, is $\epsilon$-approximable and, in general, is no harder to solve compared to the fully observable case. The approach is illustrated via two simple examples.
Chattopadhyay Ishanu
Ray Asok
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