Clempner, Julio Optimizing the decision process on Petri nets via a Lyapunov-like function. (English) Zbl 1111.91006 Int. J. Pure Appl. Math. 19, No. 4, 477-493 (2005). Summary: We introduce a new modeling paradigm for developing decision process representation called decision process Petri net (DPPN). It extends the place-transitions Petri net (PN) theoretic approach including the Markov decision processes. PNs are used for process representation taking advantage of the formal semantic and the graphical display. We optimized the utility function used for trajectory planning in the DPPN by a Lyapunov-like function, obtaining as result new characterizations for final decision points (optimum point). Illustrative examples where Lyapunov-like function properties are shown to hold are given. Cited in 1 Document MSC: 91A35 Decision theory for games 91B06 Decision theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 39A05 General theory of difference equations 39A11 Stability of difference equations (MSC2000) Keywords:stability; Lyapunov methods Software:DPPN PDFBibTeX XMLCite \textit{J. Clempner}, Int. J. Pure Appl. Math. 19, No. 4, 477--493 (2005; Zbl 1111.91006)