A Shortest-Path Lyapunov Approach for Forward Decision Processes. (4th November 2008)

• Record Type: Journal Article
• Authors: Clempner, Julio B.
• Other Names: El Rhalibi Abdennour Academic Editor.
• Is Part Of: International journal of computer games technology. Volume 2009(2009)
• Publication Date: 2008-11-04
• Subjects: Computer games -- Design -- Periodicals; Computer games -- Programming -- Periodicals; Jeux d'ordinateur; Jeux d'ordinateur -- Programmation; Computer games -- Design; Computer games -- Programming; Electronic journals; Periodicals; 794.81
• DOI: 10.1155/2009/162450
• Languages: English
• ISSNs: 1687-7047

Abstract

Abstract : 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 pointp ∗ ( M ( p ∗ ) = S < ∞ and p ∗ = ∅ ) . 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.