Method for converting dynamical systems with continuous states into Markov decision processes with discrete states
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United States of America Patent
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Apr 2, 2013
Grant Date -
Jun 30, 2011
app pub date -
Dec 29, 2009
filing date -
Dec 29, 2009
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Abstract
A continuous dynamical system is converted to a Markov decision process (MDP) with discrete states. A predetermined number of continuous states of the continuous system is selected, wherein each continuous state corresponds to one discrete state of the MDP. Delaunay triangulation is applied to the continuous states to produce a set of triangles, wherein vertices of each triangle represent the continuous states. For each discrete state, a next discrete state y=Æ’(x, a) is determined, wherein x represents the continuous state corresponding to the discrete state, a is a control action, and Æ’ is a non-linear transition function for the continuous. A particular triangle containing the next discrete state y is identified, and the next discrete state y is expressed as probabilities of transitioning to the discrete states corresponding to the continuous states x represented by the vertices of the particular triangle.
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