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Intelligent Controls for Switched Fuzzy Systems: Synthesis via Nonstandard Lyapunov Functions

  • Jinming LuoEmail author
  • Georgi M. Dimirovski
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 657)

Abstract

This paper investigates the synthesis of intelligent control algorithms for switched fuzzy systems by employing nonstandard Lyapunov functions and combined techniques. Controlled plants are assumed nonlinear and to be represented by certain specific T–S fuzzy models. In one of case studies, a two-layer multiple Lyapunov functions approach is developed that yields a stability condition for uncontrolled switched fuzzy systems and a stabilization condition for closed-loop switched fuzzy systems under a switching law. State feedback controllers with the time derivative information of membership functions are simultaneously designed. In another case, Lyapunov functions approach is developed that yields a non-fragile guaranteed cost optimal stabilization in closed-loop for switched fuzzy systems provided a certain convex combination condition is fulfilled. Solutions in both cases are found in terms of derived linear matrix inequalities, which are solvable on MATLAB platform. In another case, a single Lyapunov function approach is developed to synthesize intelligent control in which a designed switching law handles stabilization of unstable subsystems while the accompanied non-fragile guaranteed cost control law ensures the optimality property. Also, an algorithm is proposed to carry out feasible convex combination search in conjunction with the optimality of intelligent control. It is shown that, when an optimality index is involved, the intelligent controls are capable of tolerating some uncertainty not only in the plant but also in the controller implementation. For both cases of intelligent control synthesis solutions illustrative examples along with the respective simulation results are given to demonstrate the effectiveness and the achievable nonconservative performance of those intelligent controls in closed loop system architectures.

Notes

Acknowledgments

This research cooperation was generously supported in part by the NSFC of the P.R. of China (grants 61174073 and 908160028) and by the Ministry of Education & Science of the Republic Macedonia (grant 14-3145/1-17.12.2007), and also by the Fund for Science of Dogus University, Istanbul, Turkish Republic. These respective supports are gratefully acknowledged by the authors, respectively.

References

  1. 1.
    Antsaklis, P (ed.): A brief introduction to the theory and applications of hybrid systems. In: Special Issue of the IEEE Proceedings—Hybrid Systems: Theory and Applications, vol. 8, no. 7, pp. 887–897 (2000)Google Scholar
  2. 2.
    Akar, M., Ozguner, U.: Decentralized techniques for the analysis and control of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 8(6), 691–704 (2000)CrossRefGoogle Scholar
  3. 3.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Branicky, M., Bokor, V., Mitter, S.: A unified framework for hybrid control: modal and optimal control theory. IEEE Trans. Autom. Control 43(1), 31–45 (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Choi, D.J., Park, P.G.: State-feedback controller design for discrete-time switching fuzzy systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, NV, pp. 191–196 The IEEE, Piscataway, NJ, 10–13 Dec. (2002)Google Scholar
  6. 6.
    Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control 47(11), 1883–1887 (2002)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fang, C.-H., Liu, Y.-S.: A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(3), 386–397 (2006)CrossRefGoogle Scholar
  8. 8.
    Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The MathWorks, Natick, NJ (1995)Google Scholar
  9. 9.
    Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell-time. In: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, vol. 3, pp. 2655–2660. The IEEE, Piscataway, NJ, 7–10 Dec. (1999)Google Scholar
  10. 10.
    Jing, Y, Jiang, N., Zheng, Y. Dimirovski, G.M.: Fuzzy robust and non-fragile minimax control of a trailer-truck model. In: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 1221–1226. The IEEE, Piscataway, NJ, 12–14 Dec. (2007)Google Scholar
  11. 11.
    Johansson, M., Rantzer, A., Arzen, K.E.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 7(6), 713–722 (1999)CrossRefGoogle Scholar
  12. 12.
    Kogan, M.M.: Local-minimax and minimax control of linear neutral discrete system. Avtomatika i Telemehainka, vol. 11, pp. 33–44 (Automatic and Remote Control, English translations) (1997)Google Scholar
  13. 13.
    Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19, 59–70 (1999)CrossRefGoogle Scholar
  14. 14.
    Liberzon, D.: Switching in System and Control. Birkhauser, Boston, MA, USA (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    Liu, C.-H.: An LMI-based stable T-S fuzzy model with parametric uncertainties using multiple Lyapunov function approach. Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, pp. 514–519. The IEEE, Piscataway, NJ (2004)Google Scholar
  16. 16.
    Luo, J., Dimirovski, G.M., Zhao, J.: Non-fragile guaranteed cost control for a class of uncertain switched fuzzy systems. In: Proceedings of the 31st Chinese Control Conference, Hefei, Anhui, pp. 2112–2116. Chinese Association of Automation, Beijing, CN, 25–27 July (2012)Google Scholar
  17. 17.
    Luo, J., Dymirovsky, G.: A two-layer multiple Lyapunov functions stabilization control of switched fuzzy systems. In: Proceedings of the 6th IEEE Conference on Cybernetics Conference, Sofia, BG, vol. II, pp. 258–263. The IEEE and Bulgarian FNTS, Piscataway, NJ, and Sofia, BG, 6–8 Sept. (2012)Google Scholar
  18. 18.
    MathWorks, Using Matlab—Fuzzy Toolbox. The MathWorks, Natick, NJ, USAGoogle Scholar
  19. 19.
    MathWorks, Using Matlab—LMI Toolbox. The MathWorks, Natick, NJ, USAGoogle Scholar
  20. 20.
    Morse, S.: Supervisory control of families of linear set-point controllers. Part 1: exact matching. IEEE Trans. Autom. Control 41(10), 1413–1431 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Ojleska, V.M., Kolemisevska-Gugulovska, T., Dimirovski, G.M.: Influence of the state space partitioning into regions when designing switched fuzzy controllers. Facta Univ. Series Autom. Control Robot. 9(1), 103–112 (2010)MathSciNetGoogle Scholar
  22. 22.
    Ojleska, V.M., Kolemisevska-Gugulovska, T., Dimirovski, G.M.: Switched fuzzy control systems: Exploring the performance in applications. Int. J. Simul.—Syst. Sci. Technol. 12(2), 19–29 (2012)Google Scholar
  23. 23.
    Ojleska, V., Kolemisevska-Gugulovska, T., Dymirovsky, G.: Recent advances in analysis and control design for switched fuzzy systems. In: Proceedings of the 6th IEEE Conference on Cybernetics Conference, Sofia, BG, vol. II, pp. 248–257. The IEEE and Bulgarian FNTS, Sofia, BG, 6–8 Sept. (2012)Google Scholar
  24. 24.
    Ren, J.S.: Non-fragile LQ fuzzy control for a class of nonlinear desriptor systems with time delay. Proceedings of the 4th International Conference on Machine Learning and Cybernetics, Guangzhou, pp. 18–25. Institute of Intellgent Machines, Chinese Academy of Sciences, Beijng, CN, 18–25 Aug. (2005)Google Scholar
  25. 25.
    Sun, X.M., Liu, G.P., Wang, W., Rees, D.: Stability analysis for networked control systems based on average dwell time method. Int. J. Robust Nonlinear Control 20(15), 1774–1784 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man & Cybern. 15(1), 116–132 (1985)Google Scholar
  27. 27.
    Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst. 45(2), 135–156 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Tanaka, K., Ikeda, T., Wang, H.O.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans. Fuzzy Syst. 6(3), 250–265 (1998)CrossRefGoogle Scholar
  29. 29.
    Tanaka, K., Iwasaki, M., Wang, H.O.: Stability and smoothness conditions for switching fuzzy systems. In: Proceedings of the 2000 American Control Conference, Chicago, IL, pp. 2474–2478. The AACC and IEEE Press, Piscataway, NJ (2000)Google Scholar
  30. 30.
    Tanaka, K., Hori, T., Wang, H.O.: Fuzzy Lyapunov approach to fuzzy control systems design. In: Proceedings of the 20th American Control Conference, Arlington, VA, pp. 4790–4795. The AACC and IEEE Press, Piscataway, NJ, June (2001)Google Scholar
  31. 31.
    Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York, NY (2001)CrossRefGoogle Scholar
  32. 32.
    Wang, J.L., Shu, Z.X., Chen, L., Wang, Z.X.: Non-fragile fuzzy guaranteed cost control of uncertin nonlinear discrete-time systems. Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, pp. 26–31. Chinese Association of Automation, Beijing, CN, 26–31 July (2007)Google Scholar
  33. 33.
    Wang, R.J., Lin, W.W., Wang, W.J.: Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34, 1288–1292 (2004)CrossRefGoogle Scholar
  34. 34.
    Wang, R., Zhao, J.: Non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems. J. Control Theor. Appl. 23, 32–37 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Wang, W.J., Kao, C.C., Chen, C.S.: Stabilization, estimation and robustness for large-scale time-delay systems. Control Theor. Adv. Technol. 7, 569–585 (1991)MathSciNetGoogle Scholar
  36. 36.
    Yang, H., Dimirovski, G.M., Zhao, J.: Stability of a class of uncertain fuzzy systems based on fuzzy switching controller. In: Proceedings of the 25th American Control Conference, Minneapolis, MN, pp. 4067-4071. The AACC and Omnipress Inc., New York, NY, 14–16 June (2006)Google Scholar
  37. 37.
    Yang, H., Liu, H., Dimirovski, G.M., Zhao, J.: Stabilization control of a class of switched fuzzy systems. In: Proceedings of the 2007 IEEE Conference on Fuzzy Systems IEEE-FUZZ07, London, UK, pp. 1345-1350. The IEEE, Piscataway, NJ, July 23–28 (2007)Google Scholar
  38. 38.
    Yang, H., Dimirovski, G.M., Zhao, J.: Switched Fuzzy Systems: Representation modeling, stability and control design. In: Kacprzyk, J. (ed.) Chapter 9 in Studies in Computational Intelligence 109—Intelligent Techniques and Tool for Novel System Architectures, pp. 169–184. Springer, Berlin Heidelberg, DE (2008)Google Scholar
  39. 39.
    Yang, H., Zhao, J., Dimirovski, G.M.: State feedback H control design fro switched fuzzy systems. In: Proceedings of the 4th IEEE Conference on Intelligent Systems, Varna, BG, Paper 4-2/pp. 1–6. The IEEE and Bulgarian FNTS, Piscataway, NJ, and Sofia, BG, 6–8 Sept. (2008)Google Scholar
  40. 40.
    Zadeh, L.A.: Inference in fuzzy logic. IEEE Proc. 68, 124–131 (1980)CrossRefzbMATHGoogle Scholar
  41. 41.
    Zadeh, L.A.: The calculus of If-Then rules. IEEE AI Expert 7, 23–27 (1991)Google Scholar
  42. 42.
    Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178, 2751–2779 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Zak, S.H.: Systems and Control. Oxford University Press, New York, NY (2003)Google Scholar
  44. 44.
    Zhai, G.: Quadratic stabilizability of discrete-time switched systems via state and output feedback. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, vol. 3, pp. 2165-2166. The IEEE, Piscataway, NJ, 4–7 Dec. (2001)Google Scholar
  45. 45.
    Zhai, G., Lin, H., Antsaklis, P.: Quadratic stabilizability of switched linear systems with polytopic uncertainties. Int. J. Control 76(7), 747–753 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Zhang, L., Jing, Y., Dimirovski, G.M.: Fault-tolerant control of uncertain time-delay discrete-time systems using T-S models. In: Proceedings of the 2007 IEEE Conference on Fuzzy Systems IEEE-FUZZ07, London, UK 23–28, pp. 1339–1344. The IEEE, Piscataway, NJ, July (2007)Google Scholar
  47. 47.
    Zhang, L., Andreeski, C., Dimirovski, G.M., Jing, Y.: Reliable adaptive control for switched fuzzy systems. In: Proceedings of the 17th IFAC World Congress, Seoul, KO, pp. 7636–7641. The ICROS and IFAC, Seoul, KO, July 6–11 (2008)Google Scholar
  48. 48.
    Zhao, J., Spong, M.W.: Hybrid control for global stabilization of the cart-pendulum system. Automatica 37(12), 1941–1951 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Zhao, J., Dimirovski, G.M.: Quadratic stability for a class of switched nonlinear systems. IEEE Trans. Autom. Control 49(4), 574–578 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Signal State Key Laboratory of Synthetic Automation for Process IndustriesCollege of Information Science & Engineering, Northeastern UniversityShenyangPeople’s Republic of China
  2. 2.Departments of Computer and of Control & Automation EngineeringSchool of Engineering, Dogus UniversityIstanbulTurkey
  3. 3.Institute of ASE, Faculty of Electrical Eng. & Information TechnologiesSS Cyril & Methodius UniversitySkopjeRepublic of Macedonia

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