A Shortest-Path Lyapunov Approach for Forward Decision Processes
In previous work, attention was restricted to tracking the net using a backward method that knows the target point beforehand (Bellmans's equation), this work tracks the state-space in a forward direction, and a natural form of termination is ensured by an equilibrium point 𝑝∗(𝑀(𝑝∗)=𝑆<∞and𝑝∗...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Computer Games Technology |
| Online Access: | http://dx.doi.org/10.1155/2009/162450 |
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| Summary: | In previous work, attention was restricted to tracking the net using a backward method that knows the target point beforehand (Bellmans's equation), this work tracks the state-space in a forward direction,
and a natural form of termination is ensured by an equilibrium point
𝑝∗(𝑀(𝑝∗)=𝑆<∞and𝑝∗•=∅). We consider dynamical systems governed by ordinary difference equations described by Petri nets. The
trajectory over the net is calculated forward using a discrete Lyapunov-like function, considered as a distance function. Because a Lyapunov-like function is a solution to a difference equation, it is constructed to respect
the constraints imposed by the system (a Euclidean metric does not consider these factors). As a result, we prove natural generalizations of the standard outcomes for the deterministic shortest-path problem and
shortest-path game theory. |
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| ISSN: | 1687-7047 1687-7055 |