International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Controller Design for Fuzzy Systems via Piecewise Quadratic Value Functions

  • Park, Jooyoung (Department of Control and Instrumentation Engineering, Korea University) ;
  • Kim, JongHo (Department of Control and Instrumentation Engineering, Korea University)
  • Published : 2004.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper concerns controller design for the Takagi-Sugeno (TS) fuzzy systems. The design method proposed in this paper is derived in the framework of the optimal control theory utilizing the piecewise quadratic optimal value functions. The major part of the proposed design procedure consists of solving linear matrix inequalities (LMIs). Since LMIs can be solved efficiently within a given tolerance by the recently developed interior point methods, the design procedure of this paper is useful in practice. A design example is given to illustrate the applicability of the proposed method.

Keywords

References

  1. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequalities Approach, John Wiley & Sons, Inc. (New York, 2001)
  2. M. Margaliot and G. Langholz, New Approaches to Fuzzy Modeling and Control: Design and Analysis, World Scientific Publishing Co. (Singapore, 2000).
  3. J. Park, J. Kim, and D. Park, 'LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model,' Fuzzy sets and Systems 122 (2001) 73-82
  4. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Transactions on Systems, Man and Cybernetics 15 (1985) 116-132
  5. M. Johansson, A. Rantzer, and K.E. Arzen, 'Piecewise quadratic stability of fuzzy systems,' IEEE Transactions on Fuzzy Systems 7 (1999) 713-722 https://doi.org/10.1109/91.811241
  6. G. Feng, 'H$\propto$ controller design of fuzzy dynamic systems based on pecewise Lyapunov functions,' IEEE Transaction on Systems, Man, and Cybernetics-Part B: Cybernetics 34 (2004) 283-292
  7. S. Boyd, L. EIGhaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics 15, SIAM (Philadelphia, 1994)
  8. P. Gahinet, A. Nemirovski, A, J. Laub, and M. Chilali, LMJ Control Toolbox, MathWorks Inc. (Natick, MA, 1995)
  9. H. Wang, K. Tanaka., and M. Griffin, 'An approach to fuzzy control of nonlinear systems: Stability and design issues,' IEEE Transactions in Fuzzy Systems 4 (1996) 14-23 https://doi.org/10.1109/91.481841
  10. R. Sepulchre, M. Jangkovic, and P. V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag (New York, 1997)
  11. J.-J. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall (Upper Saddle River, NJ, 1990)
  12. Y. Park, M.-J. Tahk, and J. Park, 'Optimal stabilization of Takagi-Sugeno fuzzy systems with application to spacecraft control,' Journal of Guidance, Control, and Dynamics 24 (2001) 767-777 https://doi.org/10.2514/2.4777
  13. S.G. Cao, N. W. Rees, and G. Feng, 'Analysis and design of fuzzy control system using dynamic fuzzy state space models,' IEEE transactions on Fuzzy Systems 7 (1999) 192-200 https://doi.org/10.1109/91.755400