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∗((∗)=<∞and∗•=∅). 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