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Colored decision process Petri nets modeling analysis and stability. (English) Zbl 1169.93371

Summary: In this paper, we introduce a new modeling paradigm for developing a decision process representation called Colored Decision Process Petri Net (CDPPN). It extends the Colored Petri Net (CPN) theoretical approach including Markov decision processes. CPNs are used for process representation, taking advantage of the formal semantic and the graphical display. A Markov decision process is utilized as a tool for trajectory planning via a utility function. The main point of CDPPN is its ability to represent the mark-dynamic and trajectory-dynamic properties of a decision process. Within the mark-dynamic properties framework we show that CDPPN theoretical notions of equilibrium and stability are those of CPN. In the trajectory-dynamic properties framework, we optimize the utility function used for trajectory planning in CDPPN by a Lyapunov-like function, obtaining as a result new characterizations for final decision points (optimum point) and stability. Moreover, we show that CDPPN mark-dynamic and Lyapunov trajectory-dynamic properties of equilibrium, stability and final decision points converge under certain restrictions. We propose an algorithm for optimum trajectory planning that makes use of the graphical representation (CPN) and the utility function. Moreover, we consider some results and discuss possible directions for further research.

MSC:

93C83 Control/observation systems involving computers (process control, etc.)
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
90C40 Markov and semi-Markov decision processes
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