Geometric Identification and Control of Nonlinear Dynamic Systems Based on Floating Basis Vector Representation
József K. Tar*, Imre J. Rudas*, and Miklós Rontó**
*Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Budapest Tech, H-1034 Budapest, Bécsi út 96/b., Hungary
**Faculty of Science, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/A., Hungary
In this paper a simple adaptive controller is outlined that creates only temporal and situation-dependent system model. It may be a plausible alternative of the more sophisticated soft computing approaches that aim the identification of permanent and complete models. The temporal model can be built up and maintained step-by-step on the basis of slow elimination of fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation. It may be used for filling in the “lookup tables” or rule bases of the more sophisticated representations experimentally. The method applies simple elimination of the the casual algebraic singularities the occurrence of which cannot be evaded in the practice. The operation of the method is illustrated by the control of a 2 Degrees Of Freedom dynamic system as a typical paradigm via simulation.
-  Ö. Morgül, “Stabilization and disturbance rejection for the beam equation,” IEEE Trans. Automatic Control, Vol.46, No.2, pp. 1913-1918, 2001.
-  B. Guo, and Z. Luo, “Initial-boundary value problem and exponential decay for a flexible beam vibration with gain adaptive direct strain feedback control,” Nonlinear Analysis, Theory, Methods and Applications, Vol.27, No.3, pp. 353-365, 1996.
-  S. S. Ge, T. H. Lee, and G. Zhu, “Energy-based robust controller design for multi-link flexible robots,” Mechatronics, Vol.6, No.7, pp. 779-798, 1996.
-  X. Zhang, W. Xu, S. S. Nair, and V. Chellaboina, “PDE modeling and control of a flexible twolink manipulator,” IEEE Tran. Control System Technology, Vol.13, No.2, pp. 301-312, March, 2005.
-  P. V. Kokotovic, H. K. Khalil, and J. O’Reilly, “Singular Perturbation Methods in Control: Analysis and Design,” New York, Academic Press, 1986.
-  J. Lin, and F. L. Lewis, “Two-time scale fuzzy logic controller of flexible link robot arm,” Fuzzy Sets and Systems, Vol.139, pp. 125-149, 2003.
-  “The Mechatronics Handbook,” Editor-in-Chief: H. R. Bishop, common issue by ISA – The Instrumentation, Systems, and Automation Society and CRC Press, Boca Raton London New York Washington D.C., ISBN: 0-8493-0066-5, 2002.
-  “Intelligent Control Systems Using Soft Computing Methodologies,” Eds. Ali Zilouchian & Mo Jamshidi, CRC Press, Boca Raton London New York Washington D.C., ISBN: 0-8493-1875-0, 2001.
-  H. O.Wang, K. Tanaka, and M. F. Griffin, “Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model,” in Proceedings of the FUZZ-IEEE/IFES’95, pp. 531-538, 1995.
-  H. O. Wang, K. Tanaka, and M. F. Griffin, “An analytical framework of fuzzy modeling and control of nonlinear systems: stability and design issues,” in Proceedings of the 1995 American Control Conference, Seattle, pp. 2272-2276, 1995.
-  K. Tanaka, T. Ikeda, and H. O. Wang, “Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory and linear matrix inequalities,” IEEE Tran. Fuzzy Systems, Vol.4, No.1, pp. 1-13, February, 1996.
-  I. Kováčová, L. Madarász, D. Kováč, and J. Vojtko, “Neural Network Linearization of Pressure Force Sensor Transfer Characteristics,” Proc. of the 8th International Conference on Intelligent Engineering Systems 2004 (INES’04), Technical University of Cluj-Napoca Romania, pp. 79-82, ISBN 973-662-120-0, September 19-21, 2004.
-  J. S. Jang, “Self-Learning Fuzzy Controllers Based on Temporal Back Propagation,” IEEE Trans. on Neural Networks, Vol.3, No.5, 1992.
-  J. S. Jang, and C. Sun, “Neuro-Fuzzy Modeling and Control,” Proc. of IEEE, Vol.83, No.3, pp. 378-406, 1995.
-  “Fuzzy Logic Toolbox User’s Guide,” Math Works, Inc., 1995.
-  J. Moody, and C. Darken, “Fast Learning in Networks of Locally-Tuned Processing Units,” Neural Computation, Vol.1, pp. 281-294, 1989.
-  M. Clerc, and J. Kennedy, “The particle swarm-explosion, stability and convergence in a multidimensional complex space,” IEEE Tran. Evolutionary Computation, Vol.6, No.1, pp. 58-73, February, 2002.
-  Y. Shi, and R. C. Eberhart, “Empirical study of particle swarm optimization,” in Proceedings of the 1999 Congr. Evolutionary Computation, IEEE Service Center, Piscataway, NJ, pp. 1945-1950, 1999.
-  J. Vaščák, and L. Madarász, “Similarity Relations in Diagnosis Fuzzy Systems,” Journal of Advanced Computational Intelligence, Vol.4, No.4, Fuji Press, Japan, ISSN 1343-0130, pp. 246-250, 2000.
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