Copyright © 2008 The Institute of Electronics, Information and Communication Engineers
Regular Section -- Letters -- Systems and Control |
Efficient Calculation of the Transition Matrix in a Max-Plus Linear State-Space Representation
1 The author is with Nagaoka University of Technology, Nagaoka-shi, 940-2188 Japan. E-mail: hgoto{at}kjs.nagaokaut.ac.jp
This research considers an efficient method for calculating the transition matrix in an MPL (Max-Plus Linear) state-space representation. This matrix can be generated by applying the Kleene star operator to an adjacency matrix. The proposed method, based on the idea of a topological sort in graph theory and block splitting, is able to calculate the transition matrix efficiently.
Key Words: max-plus linear representation, directed acyclic graph, adjacency matrix, Kleene star, topological sort
Manuscript received September 10, 2007. Manuscript revised January 30, 2008.
References
[1] B. Heidergott, G.J. Olsder, and L. Woude, Max Plus at Work: Modeling and Analysis of Synchronized Systems, Princeton University Press, New Jersey, 2006. [2] F. Baccelli, G. Cohen, G.J. Olsder, and J.P. Quadrat, Synchronization and Linearity, John Wiley & Sons, New York, 1992. http://maxplus.org [3] G. Schullerus, V. Krebs, B. Schutter, and T. Boom, "Input signal design for identification of max-plus-linear-systems," Automatica, vol.42, pp.937–943, 2006. [4] A. Moh, M. Manier, H. Manier, and A. Moudni, "A max-plus algebra modeling for a public transport system," Cybernetics and Syst., vol.36, pp.1–16, 2005. [5] H. Goto, "Dual representation of event-varying max-plus linear systems," Int. J. Comput. Sci., vol.1, no.3, pp.225–242, 2007. [6] H. Goto and S. Masuda, "Consideration of capacity and order constraints for event-varying MPL systems," IEICE Trans. Fundamentals, vol.E90-A, no.9, pp.2024–2028, Sept. 2007. [7] T. Cormen and C. Leiserson, Introduction to Algorithms, MIT Press, Massachusetts, 2001. [8] R Development Core Team: R: A Language and Environment for Statistical Computing, R Foundation Stat. Comput., Vienna, 2007. http://www.R-project.org
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