State Feedback Controller Design via Takagi- Sugeno Fuzzy Model: LMI Approach

Authors: F. Khaber, K. Zehar, A. Hamzaoui

Abstract:

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079430

References:

[1] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia,PA, 1994.
[2] K. Tanaka and H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, 2001.
[3] H.O. Wang, K. Tanaka, and M.F. Griffin, "An approach to fuzzy control of nonlinear systems: stability and design issues," IEEE Trans. Fuzzy Systems, vol. 4, N┬░1, pp. 14-23, 1996.
[4] J. Zhao, V. Wertz, and R. Gorez, "Dynamic Fuzzy state feedback Controller and Its limitations," Proc. American Contr. Conf., pp. 121- 126,1996.
[5] K. Tanaka and M. Sugeno, "Stability analysis and design of fuzzy control systems," Fuzzy Sets and Systems, vol. 45, pp. 135 -156, 1992.
[6] Y. Nesterov and A. Nemirovski, Interior Point Polynomial Methods in Convex Programming: Theory and Applications, SIAM, Philadelphia,PA, 1994.
[7] K. Tanaka, T. Ikeda, and H.O. Wang, "Fuzzy control system design via LMIs," Proc. American Contr. Conf., vol. 5, pp. 2873 -2877, 1997.
[8] K. Tanaka, T. Ikeda, and H.O. Wang, "Design of fuzzy control system based on relaxed LMI Stability conditions," Proc. 35th CDC, pp. 598-603, 1996.
[9] P. Dorato, C.T. Abdallah, and V. Cerone, Linear Quadratic Control: An Introduction, PrenticeHall, Englewood Cliffs, NJ, 1995.
[10] 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 Trans. Fuzzy Systems, vol. 4, pp. 1-13, 1996.
[11] P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995.
[12] N. E. Mastorakis, "Modeling dynamical systems via the Takagi-Sugeno fuzzy model," Proceedings of the 4th WSEAS International Conference on Fuzzy sets and Fuzzy Systems, Udine, Italy, march 25-27, 2004.
[13] F. Khaber, A. Hamzaoui, and K. Zehar, "LMI Approach for robust fuzzy control of uncertain nonlinear systems," 2nd International Symposium on Hydrocarbons & Chemistry, Algeria, March 21-23, 2004.
[14] C. Scherer, S. Weiland. (2004, November 16). Linear Matrix Inequalities in Control (Online) Available: http://www.cs.ele.tue.nl/sweiland/lmi.html