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Discrete Event Dynamic Systems

, Volume 24, Issue 4, pp 447–471 | Cite as

Exact and approximate approaches to the identification of stochastic max-plus-linear systems

  • Samira S. Farahani
  • Ton van den Boom
  • Bart De Schutter
Article

Abstract

Stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra, belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. In this paper, we study the identification problem for such systems, considering two different approaches. One approach is based on exact computation of the expected values and consists in recasting the identification problem as an optimization problem that can be solved using gradient-based algorithms. However, due to the structure of stochastic max-plus linear systems, this method results in a complex optimization problem. The alternative approach discussed in this paper, is an approximation method based on the higher-order moments of a random variable. This approach decreases the required computation time significantly while still guaranteeing a performance that is comparable to the one of the exact solution.

Keywords

Stochastic discrete event systems System identification Stochastic max-plus-linear systems Analytic integration Approximation Moments 

Notes

Acknowledgements

The authors would like to thank Dr. Ioan Landau for his useful comments and suggestions and Dr. Hans van der Weide for his help in the derivation of the approximation method presented in Farahani et al. (2010). This research is partially funded by the Dutch Technology Foundation STW project “Model-predictive railway traffic management” (11025), and by the European Union Seventh Framework Programme [FP7/2007-2013] under grant agreement no. 257462 HYCON2 Network of Excellence.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Samira S. Farahani
    • 1
  • Ton van den Boom
    • 1
  • Bart De Schutter
    • 1
  1. 1.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands

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