TY - JOUR A2 - El Rhalibi, Abdennour AU - Clempner, Julio B. PY - 2009 DA - 2009/01/15 TI - A Shortest-Path Lyapunov Approach for Forward Decision Processes SP - 162450 VL - 2009 AB - 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<andp=). We consider dynamical systems governed by ordinary difference equations described by Petri nets. Thetrajectory 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 respectthe 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 andshortest-path game theory. SN - 1687-7047 UR - https://doi.org/10.1155/2009/162450 DO - 10.1155/2009/162450 JF - International Journal of Computer Games Technology PB - Hindawi Publishing Corporation KW - ER -