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2005 | 15 | 3 | 405-420
Tytuł artykułu

Colored decision process Petri nets: modeling, analysis and stability

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we introduce a new modeling paradigm for developing a decision process representation called the Colored Decision Process Petri Net (CDPPN). It extends the Colored Petri Net (CPN) theoretic 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 the 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 theoretic notions of equilibrium and stability are those of the CPN. In the trajectory-dynamic properties framework, we optimize the utility function used for trajectory planning in the 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.
Rocznik
Tom
15
Numer
3
Strony
405-420
Opis fizyczny
Daty
wydano
2005
otrzymano
2005-03-16
poprawiono
2005-07-19
Twórcy
  • Center for Computing Research National Polytechnic Institute (CIC-IPN), Av. Juan de Dios Batiz s/n, Edificio CIC Col. Nueva Industrial Vallejo, 07-738 Mexico City, Mexico
Bibliografia
  • Bellman R.E. (1957): Dynamic Programming. - Princeton, N.J.: Princeton Univ. Press.
  • Clempner J. (2005): Optimizing the decision process on Petrinets via a Lyapunov-like function. - Int. J. Pure Appl.Math., Vol. 19, No. 4, pp. 477-494.
  • Clempner J., Medel J. and Carsteanu A. (2005): Extending games with local and robust Lyapunov equilibrium and stability condition.- Int. J. Pure Appl. Math., Vol. 19, No. 4, pp. 441-454.
  • Howard R.A. (1960): Dynamic Programming and Markov Processes. - Cambridge: MIT Press.
  • Jensen K. (1981): Coloured Petri Nets and the Invariant Method. - North-Holland Publishing Company.
  • Jensen K. (1986): Coloured Petri Nets. - Tech. Rep., Computer Science Department, Aarhus University, Denmark.
  • Jensen K. (1994): An Introduction to the Theoretical Aspects of Coloured Petri Nets. - Lecture Notes in Computer Science, Vol. 803, Berlin: Springer.
  • Jensen K. (1997a): Coloured Petri Nets, Vol. 1. - Berlin: Springer.
  • Jensen K. (1997b): Coloured Petri Nets, Vol. 2. - Berlin: Springer.
  • Kalman R.E. and Bertram J.E. (1960): Control system analysis and design via the 'Second Method' of Lyapunov. - J. Basic Eng., Vol. 82, pp. 371-393.
  • Lakshmikantham V., Leela S. and Martynyuk A.A. (1990): Practical Stability of Nonlinear Systems. - Singapore: World Scientific.
  • Lakshmikantham V., Matrosov V.M. and Sivasundaram S. (1991): Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems. - Dordrecht: Kluwer.
  • Massera J.L. (1949): On Lyapunoff's coonditions of stability- Ann. Math., Vol. 50, No. 3, pp. 705-721.
  • Murata T., (1989): Petri Nets Properties, analysis and applications. - Proc. IEEE, Vol. 77, No. 4, pp. 541-580.
  • Passino K.M., Burguess K.L. and Michel A.N. (1995): Lagrange stability and boundedness of discrete event systems. - J. Discr. Event Syst. Theory Appl., Vol. 5, pp. 383-403.
  • Puterman M.L. (1994): Markov Decision Processes: Discrete Stochastic Dynamic Programming. - New York: Wiley.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv15i3p405bwm
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