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Abstrakty
This paper introduces a novel approach to BIBO stability of NARX control systems. The approach is based on difference inequalities and assumes availability of an approximate NARX model and the system order. Sufficient conditions for modelling error are derived ensuring boundedness of the error between model's and plant's outputs for the same inputs. For this class of bounded inputs sufficient conditions for BIBO stability are given and shown practicable. They also allow designing a controller using the model, leading to BIBO stable closed-loop system.
Słowa kluczowe
Rocznik
Tom
Strony
295--311
Opis fizyczny
Bibliogr. 23 poz., 1 tab.
Twórcy
autor
- Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa, Poland (Instytut Sterowania i Elektroniki Przemysłowej, Politechnika Warszawa)
Bibliografia
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- [2] S. Chen, S.A. Billings, Representations of non-linear systems: the NARMAX model, International Journal of Control, 49, 3, (1989) 1013-1032.
- [3] S. Chen, S.A. Billings, P.M. Grant, Non-linear system identification using neural networks, International Journal of Control, 51 (1990) 1191-1214.
- [4] S. Chen, S.A. Billings, C.F. Cowan, P.M. Grant, Practical identification of NARMAX models using radial basis functions, International Journal of Control, 52 (1990) 1327-1350.
- [5] K.S. Narendra, K. Parthasarathy, Gradient methods for the optimization of dynamical systems containing neural networks, IEEE Transactions on Neural Networks, 2 (1991) 252-262.
- [6] R. Zbikowski, A. Dzielitiski, Nonuniform sampling approach to control systems modelling with feedforward networks, in Neural adaptive control technology (R. Zbikowski and K. J. Hunt, eds.), World Scientific Series in Robotics and Intelligent Systems, 15 (1996) 71-112, Singapore: World Scientific.
- [7] A. Dzielinski, R. Zbikowski, A new approach to neurocontrol based on Fourier analysis and nonuniform multi-dimensional sampling, Applied Mathematics and ComputerScience, 6, 3, (1996) 101-121.
- [8] C. A. Desoer, M. Vidyasagar, Feedback systems: input-output properties, New York: Academic Press, 1975.
- [9] M. Vidyasagar, Nonlinear systems analysis, Englewood Cliffs: Prentice-Hall, Second ed., 1992.
- [10] J.C. Kalkkuhl, K.J. Hunt, Discrete-time neural model structures for continuous nonlinear systems: fundamental properties and control aspects, in Neural adaptive control technology (R. Zbikowski and K. J. Hunt, eds.), World Scientific Series in Robotics and Intelligent Systems, 15, 3-40, Singapore: World Scientific, 1996.
- [11] A. U. Levin, K.S. Narendra, Identification using feedforward Networks, Neural Computation, 7, 2, (1995) 349-357.
- [12] K. J. Astrom, B. Wittenmark, Adaptive control, Reading, Massachusetts: Addison-Wesley, Second ed., 1995.
- [13] G. Zames, Input-output feedback stability and robustness, 1959-85, IEEE Control Systems Magazine, 16 (1996) 61-66.
- [14] V. Fromion, 8S. Monaco, D. Normand-Cyrot, A Link between input-output stability and Lyapunov stability, Systems Control Letters, 27 (1996) 243-248.
- [15] K.S. Narendra, A.M. Annaswamy, Stable adaptive systems, Eglewood Cliffs, NJ: Prentice-Hall 1989.
- [16] V. Lakshmikantham, D. Trigiante, Theory of difference equations: numerical methods and applications, Boston: Academic Press, 1988.
- [17] B.G. Pachpatte, On some n-th order finite difference inequalities, Proceedings of the National Academy of Sciences, India, Section A, 40 (1970) 235-240.
- [18] R. P. Agarwal, Properties of solutions of higher order nonlinear difference equations. I, Analele Stiintifice ale Universitatii Al. I. Cuza” din Iasi (Serie Noua), Matematica, XXXI, 2, (1985) 165-172.
- [19] R. P. Agarwal, Difference equations and inequalities. Theory, methods, and applications, New York: Marcel-Dekker, Inc., 1992.
- [20] K. Knopp, Theory and application of infinite series, New York: Dover Publications, Inc., 1990. (Reprint of the 1951 second English edition).
- [21] H.G. Eggleston, Elementary real analysis, Cambridge: Cambridge University Press, 1962.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG1-0010-0054