Abstract.In this paper we introduce a new modeling paradigm for optimazing the trajectory planning using decision process Petri nets (DPPN). The main point of the DPPN 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 the DPPN theoretic notions of equilibrium and stability are those of the place-transitions Petri net. In the trajectory-dynamic properties framework, we optimized the utility function used for trajectory planning in the DPPN via a Lyapunov-like function, obtaining as a result new characterizations for final decision points (optimum point) and stability. Moreover, we show that the DPPN mark-dynamic and Lyapunov trajectory-dynamic properties of equilibrium, stability an final decision points (optimum point) converge under certain restrictions. We propose an algorithm for optimum trajectory planning, that makes use of the graphical representation of the place-transitions Petri net and the utility function. Application examples are presented.

Received: June 2, 2005

AMS Subject Classification: 62C99, 91A35, 91B06, 93D005, 39A05, 39A11

Key Words and Phrases: decision process, decision process Petri nets, stability, Lyapunov methods, optimization, game theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 4