Switching Model Construction and Stability Analysis for Nonlinear Systems
Hiroshi Ohtake, and Kazuo Tanaka
Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
This paper presents switching model construction and stability analysis for a class of nonlinear systems. A switching fuzzy model newly developed in this paper is employed to represent the dynamics of a nonlinear system. A key feature of the switching fuzzy model construction is to find the so-called minimum distance sector by solving a nonlinear optimization problem. Next, we discuss the stability of a switching fuzzy model. To take advantage of the switching fuzzy model, we introduce a piecewise Lyapunov function that mirrors its structure. We show that the piecewise Lyapunov function approach provides less conservative results for the typical quadratic Lyapunov function approach. Illustrative examples demonstrate the utility of the switching model construction and the stability analysis.
-  H. K. Khalil, “Nonlinear Systems,” Prentice Hall, Upper Saddle River, NJ, Third Edition, 2002.
-  K. Tanaka, and H. O. Wang, “Fuzzy Control Systems Design and Analysis,” Wiley-Interscience, 2001.
-  K. Tanaka, and M. Sugeno, “Stability Analysis and Design of Fuzzy Control System,” Fuzzy Sets And Systems, Vol.45, No.2, pp. 135-156, 1992.
-  H. O. Wang, K. Tanaka, and M. Griffin, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues,” IEEE Transactions on Fuzzy Systems, Vol.4, No.1, pp. 14-23, 1996.
-  K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI based Designs,” IEEE Transactions on Fuzzy Systems, Vol.6, No.2, pp. 250-265, 1998.
-  D. Filev, “Algebraic Design of Fuzzy Logic Controllers,” Proceeding of 1996 IEEE International Symposium on Intelligent Control, pp. 253-258, 1996.
-  D. Filev, “Gain scheduling based control of a class of TSK systems,” in Fuzzy Control, Synthesis and Analysis, edited by S. Farinwata, D. Filev, and R. Langari, John Wiley & Sons, Ltd, Chichester, England, pp. 321-334, 2000.
-  S. K. Hong, and R. Langari, “Robust Fuzzy Control of Magnetic Bearing System Subject to Harmonic Disturbances,” IEEE Transactions on Control Systems Technology, Vol.8, No.2, pp. 366-371, Mar., 2000.
-  G. Kang, W. Lee, and M. Sugeno, “Design of TSK fuzzy controller based on TSK fuzzy model using pole placement,” Proceeding of the 7th IEEE International Conference on Fuzzy Systems, pp. 246-251, Anchorage, AK, 1998.
-  H. Ying, and G. Chen, “Analytical Theory of Fuzzy Control with Applications,” Information Sciences, Vol.123, No.3-4, pp. 161-162, 2000.
-  L. Chen, G. Chen, and Y. W. Lee, “Fuzzy Modeling and Adaptive Control of Uncertain Chaotic Systems,” Information Sciences, Vol.121, No.1-2, pp. 27-37, 1999.
-  G. Chen, and D. Zhang, “Back-Driving a Truck with Suboptimal Distance Trajectories: A Fuzzy Logic Control Approach,” IEEE Transactions on fuzzy systems, Vol.5, No.3, pp. 369-380, Aug., 1997.
-  D. Filev, and P. Angelov, “Fuzzy Optimal Control,” Fuzzy Sets and Systems, Vol.47, pp. 151-156, 1992.
-  R. Langari, and M. Tomizuka, “Analysis and Synthesis of Fuzzy Linguistic Control Systems,” Proceeding of the 1990 ASME Winter Annual Meeting, pp. 35-42, 1990.
-  R. Langari, “A Nonlinear Formulation of a Class of Fuzzy Linguistic Control Algorithms,” Proceeding of the 1992 American Control Conference, pp. 2273-2278, Chicago, IL, 1992.
-  Y. Huang, and S. Yasunobu, “A General Predictive Fuzzy Control with Disturbance Rejection Property and its Application to the Time-delay nonlinear System,” Proceeding of the 8th IFSA World Congress, pp. 524-527, Taipei, Taiwan, 1999.
-  Y. Huang, and S. Yasunobu, “A General Practical Design Method for Fuzzy PID Control from Conventional PID Control,” Proceeding of the 9th IEEE International Conference on Fuzzy Systems, Vol.2, pp. 969-972, San Antonio, Texas, 2000.
-  M. Sugeno, “On Stability of Fuzzy Systems Expressed by Fuzzy Rules with Singleton Consequents,” IEEE Transactions on Fuzzy Systems, Vol.7, No.2, pp. 201-224, April, 1999.
-  H. Yamamoto, and T. Furuhashi, “A new sufficient condition for stable fuzzy control system and its design method,” IEEE Transactions on Fuzzy Systems, Vol.9, No.2, pp. 554-569, 2001.
-  T. Furuhashi, et al., “Fuzzy Control Stability Analysis Using Generalized Fuzzy Petri Net Model,” Journal of Advanced Computational Intelligence, Vol.3, No.2, pp. 99-105, 1999.
-  T. Hasegawa, and T. Furuhashi, “Stability Analysis of Fuzzy Control Systems Simplified as a Discrete System,” International Journal of Control and Cybernetics, Vol.27, No.4, pp. 565-577, 1998.
-  T. Takagi, and M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Transactions on Systems, Man and Cybernetics, Vol.15, pp. 116-132, 1985.
-  M. Johansson, “Piecewise Linear Control Systems,” Ph.D. Thesis, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1999.
-  K. Tanaka, T. Hori, and H. O. Wang, “A Fuzzy Lyapunov Approach to Fuzzy Control System Deign,” Proceeding of 2001 American Control Conference, pp. 4790-4795, Arlington, 2001.
-  H. Ohtake, K. Tanaka, and H. O. Wang, “Fuzzy Modeling via Sector Nonlinearity Concept,” Integrated Computer-Aided Engineering, Vol.10, No.4, pp. 333-341, 2003.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.