Circuits, Systems and Signal Processing

, Volume 17, Issue 3, pp 401–419 | Cite as

Hybrid control system design using a fuzzy logic interface

  • Rafael Fierro
  • Frank L. Lewis
  • Kai Liu


A hybrid control system is proposed for regulating an unknown nonlinear plant. The interface between the continuous-state plant and the discrete-event supervisor is designed using a fuzzy logic approach. The fuzzy logic interface partitions the continuous-state space into a finite number of regions. In each region, the original unknown nonlinear plant is approximated by a fuzzy logic-based linear model, then state-feedback controllers are designed for each linear model. A high-level supervisor coordinates (mode switching) the set of closed-loop systems in a stable and safe manner. The stability of the system is studied using nonsmooth Lyapunov functions. For illustration and verification purposes, this technique has been applied to the well-known inverted pendulum balancing problem.


Linear Model System Design Fuzzy Logic Finite Number Lyapunov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    P. Antsaklis, M. Lemmon, and J. A. Stiver, Modeling and design of hybrid control systems,Proc. IEEE Mediterranean Symp. on New Directions in Control & Automation, Krete, Greece, June 1994, pp. 440–447.Google Scholar
  2. [2]
    P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, eds.,Hybrid Systems II, Lecture Notes in Computer Science, vol. 999, Springer, New York, 1995.Google Scholar
  3. [3]
    B. R. Barmish,New Tools for Robustness of Linear Systems, Macmillan, New York, 1994.Google Scholar
  4. [4]
    M. S. Branicky, Topology of hybrid systems,Proc. IEEE Conf. Dec. Contr., San Antonio, TX, Dec. 1993, pp. 2309–2314.Google Scholar
  5. [5]
    M. S. Branicky, Stability of switched and hybrid systems,Proc. IEEE Conf. Dec. Contr., Lake Buena Vista, FL, Dec. 1994, pp. 3498–3503.Google Scholar
  6. [6]
    M. Dogruel and Ü. Özgüner, Modeling and stability issues in hybrid systems, in[2],, 1995, pp. 148–165.Google Scholar
  7. [7]
    R. Fierro and F. L. Lewis, A framework for hybrid control design,IEEE Trans. Syst., Man, Cyber., vol. 27-A, no. 6, 1997, to appear.Google Scholar
  8. [8]
    R. Fierro, F. L. Lewis, and C. T. Abdallah, Common, multiple and parametric Lyapunov functions for a class of hybrid dynamical systems,Proc. IEEE Mediterranean Symp. on New Directions in Control & Automation, Krete, Greece, June 1996, pp. 77–82.Google Scholar
  9. [9]
    A. F. Filippov,Differential Equations with Discontinuous Righthand Sides, Kluwer Academic Publishers, Dordrecht, 1988.Google Scholar
  10. [10]
    L. El Ghaoui, R. Nikoukhah, and F. Delebecque, LMITOOL: A package for LMI optimization,Proc. IEEE Conf. Dec. Contr., New Orleans, LA, Dec. 1995, pp. 3096–3101.Google Scholar
  11. [11]
    H. K. Khalil,Nonlinear Systems, Macmillan, New York, 1992.Google Scholar
  12. [12]
    M. Lemmon and C. Bett, Robust hybrid control system design,Proc. IFAC 13th Triennial World Congress, San Francisco, June 1996, pp. 395–400.Google Scholar
  13. [13]
    K. Liu and F. L. Lewis, Adaptive tuning of fuzzy logic identifier for unknown nonlinear systems,Int. J. Adaptive Control and Signal Processing, vol. 8, pp. 573–586, 1994.Google Scholar
  14. [14]
    J. Lygeros, A formal approach to fuzzy modeling, Tech. Rep. UCB/ERL M95/15, Electronics Research Laboratory, University of California Berkeley, March 1995.Google Scholar
  15. [15]
    J. Malmborg, B. Bernhardsson, and K. J. Aström, A stabilizing switching scheme for multicontroller systems,Proc. IFAC 13th Triennial World Congress, San Francisco, CA, June 1996, pp. 229–234.Google Scholar
  16. [16]
    J. M. Mendel, Fuzzy logic systems for engineering: A tutorial,Proc. IEEE, vol. 83, no. 3, pp. 345–377, 1995.Google Scholar
  17. [17]
    A. Nerode and W. Kohn, Models for hybrid systems: Automata, topologies, controllability, observability,Hybrid Systems, Lecture Notes in Computer Science, R. Grossman, A. Nerode, A. Ravn, and H. Rischel, eds., vol. 736, Springer, New York, 1993, pp. 317–356.Google Scholar
  18. [18]
    P. Peleties and R. A. DeCarlo, Asymptotic stability of m-switched systems based on Lyapunov-like functions,Proc. American Contr. Conf., Boston, MA, June 1991, pp. 1679–1683.Google Scholar
  19. [19]
    W. A. Sethares, B. D. O. Anderson, and C. R. Johnson, Jr., Adaptive algorithms with filtered regressor and filtered error,Math. Contr. Sig. Syst., no. 2, pp. 381–403, 1989.Google Scholar
  20. [20]
    J. Shamma and M. Athans, Guaranteed properties of gain scheduled control for linear parametervarying plants,Automatica, vol. 27, no. 3, pp. 559–564, 1991.Google Scholar
  21. [21]
    D. Shevitz and B. Paden, Lyapunov stability theory of nonsmooth systems,IEEE Trans. Autom. Contr., vol. 39, no. 9, pp. 1910–1914, 1994.Google Scholar
  22. [22]
    J. E. Slotine and W. Li,Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, 1991.Google Scholar
  23. [23]
    K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems,Fuzzy Sets Syst., vol. 45, no. 2, pp. 135–156, 1992.Google Scholar
  24. [24]
    H. O. Wang, K. Tanaka, and M. F. Griffin, An approach to fuzzy control of nonlinear systems: Stability and design issues,IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14–23, 1996.Google Scholar
  25. [25]
    H. Ye, A. N. Michel, and L. Huo, Stability theory for hybrid dynamical systems,Proc. IEEE Conf. Dec. Contr., New Orleans, LA, Dec. 1995, pp. 2679–2684.Google Scholar

Copyright information

© Birkhäuser 1998

Authors and Affiliations

  • Rafael Fierro
    • 1
  • Frank L. Lewis
    • 1
  • Kai Liu
    • 1
  1. 1.Automation and Robotics Research InstituteThe University of Texas at ArlingtonFort Worth

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