Abstract
The problem of Systems Identification starts with a timeseries of observed data and tries to determine the simplest model capable of exhibiting the observed behavior. This optimization problem searches the model from a space of possible models. In traditional methods, the search space is the set of numerical values to be assigned to parameters. In our approach we are constrained, and therefore limit the search space, to Linear Time-Invariant models. In this paper, we present the theory and algorithms to perform Qualitative Systems Identification for Linear Time Invariant Dynamic Systems. The methods described here are based on successive elimination of the components of the system’s response. Sinusoidals of high frequencies are eliminated first, then their carrying waves. We continue with the process until we obtain a nonoscillatory carrier. At that point, we determine the order of the carrier. This procedure allows us to determine how many sinusoidal components, and how many exponential components are found in the impulse response of the system under study. The number of components determines the order of the system. The paper is composed of two important parts, the statement of some mathematical properties of the responses of Linear Time Invariant Dynamic Systems, and the proposal of a set of filters that allows us to implement the recognition algorithm.
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References
W.E. Boyce and R.C. DiPrima. Elementary Differential Equations. John Wiley, New York, second edition, 1969.
C.J. Downing, B. Byrne, K. Coveney, and W.P. Marnane. Controller optimisation and system identification using genetic algorithms. Technical report, Dept. of Electrical Engineering University College Cork., 1996.
Juan J. Flores and Art M. Farley. Reasoning about constant coeficient dynamic systems. In Proc. 9th Int. Workshop on Qualitative Reasoning About Physical Systems, Amsterdam, The Netherlands, May, 1995.
David E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, Boston, 1998.
Randy L. Haupt and Sue Ellen Haupt. Practical Genetic Algorithms. Wiley Interscience, New York, 1998.
K.J. Hunt. Black-box and partially known system identification with genetic algorithms. In European Control Conference, Savoy Place, London WC2R 0BL, UK, 1993.
K. Kristinsson and G.A. Dumont. System identification and control using genetic algorithms. IEEE Trans. Syst. Man Cybern., 22(5):1033–1046, 1992.
Lenart Ljung. System Identification: Theory for the user. Prentice-Hall, Englewood Cliffs, NJ, 1987.
Soderstrom T. Stoica P. System Identification. Prentice Hall, USA, 1989.
Nelio Pastor. Identificacion de sistemas dinamicos utilizando algoritmos geneticos. Master’s thesis, School of Electrical Engineering, University of Michoacan, Morelia, Mexico, 2000.
Fazel Naghdy Zang Zibo. Application of Genetic Algorithms to System Identification. Departament of Electrical and Computer Engineering University of Wollogong, Australia, 1987.
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© 2002 Springer-Verlag Berlin Heidelberg
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Flores, J.J., Pastor, N. (2002). Qualitative Systems Identication for Linear Time Invariant Dynamic Systems. In: Coello Coello, C.A., de Albornoz, A., Sucar, L.E., Battistutti, O.C. (eds) MICAI 2002: Advances in Artificial Intelligence. MICAI 2002. Lecture Notes in Computer Science(), vol 2313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46016-0_49
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DOI: https://doi.org/10.1007/3-540-46016-0_49
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