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Optimizing the decision process on Petri nets via a Lyapunov-like function. (English) Zbl 1111.91006

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.

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)

Software:

DPPN
PDFBibTeX XMLCite