A switching controller design via sum-of-squares approach for a class of polynomial T-S fuzzy model

International Journal of Innovative Computing, Information and Control

Volumn 7, Issue 7 B, 2011, Pages 4363-4376

  Chen, Shun Hung ^a   Juang, Jyh Ching ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Polynomial T S fuzzy; Sum of squares programming; Switch controller

Indexed keywords

FUZZY MODELS; LINEARIZATION ERRORS; NON-LINEAR CONTROLLERS; NONLINEAR FUZZY CONTROL; POLYNOMIAL REPRESENTATIONS; REGION OF CONVERGENCE; SUM OF SQUARES; SUM-OF-SQUARES PROGRAMMING; SUM-OF-SQUARES TECHNIQUES; SWITCHING CONTROL; SWITCHING CONTROLLERS; T-S FUZZY; T-S FUZZY MODELS; TAKAGI SUGENO FUZZY MODELS;

BLENDING; COMPUTER CONTROL SYSTEMS; COMPUTER SIMULATION; CONTROLLERS; FUZZY CONTROL; POLYNOMIALS; SEMICONDUCTOR SWITCHES; SWITCHING SYSTEMS; SYSTEMS ENGINEERING;

MATHEMATICAL MODELS;

EID: 79959881147     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. A. Alleyne, Physical insights on passivity-based TORA control designs, IEEE Transactions on Control Systems Technology, vol.6, no.3, pp.436-439, 1998.
2. M. S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, vol.43, no.4, pp.475-482, 1998.
3. W. J. Chang and S. M. Wu, State variance constrained fuzzy controller design for nonlinear TORA systems with minimizing control input energy, Proc. of the 2003 IEEE International Conference on Robotics and Automation, pp.2616-2621, 2003.
4. S. Chen, B. Mulgrew and P. M. Grant, TORA example: Cascade and passivity control design, Proc. of 1995 America Control Conference, pp.4347-4351, 1995.
5. J. U. Duncombe, A benchmark problem for nonlinear control design: Problem statement, experimental testbed, and passive nonlinear compensation, Proc. of 1995 America Control Conference, pp.4363-4367, 1995.
6. H. Y. Chung and S. H. Chan, Stability analysis of fuzzy control systems using polynomial methods, International Journal of Innovative Computing, Information and Control, vol.5, no.11, pp.3733-3744, 2009.
7. B. Hu, X. Xu, A. N. Michel and P. J. Antsaklis, Stability analysis for a class of nonlinear switched systems, Proc. of the 38th Conf. on Decision and Control, pp.4374-4379, 1999.
8. Z. Jarvis-Wloszek, R. Feeley, W. Tan, K. Sun and A. Packard, Some controls applications of sum of squares programming, Proc. of the 42nd IEEE Conf. on Decision and Control, vol.5, pp.4676-4681, 2003.
9. D. J. Leith, Survey of gain-scheduling analysis and design, International Journal of Control, vol.73, no.11, pp.1001-1025, 2000.
10. D. Liberzon and A. S. Morse, Basic problems in stability and design of switched systems, IEEE Control Magazine, vol.19, no.5, pp.59-70, 1999.
11. C. L. Lin and H. W. Su, Intelligent control in guidance and control system design: An overview, Proc. of National Science Council ROC(A), vol.24, no.1, pp.15-30, 2000.
12. R. Ortega, A. Loria, P. J. Nicklasson and H. Sira-Ramirez, Passivity-Based Control of Euler- Lagrange System: Mechanical, Electrical, and Electromechanical Applications, Springer, 1998.
13. A. Papachristodoulou and S. Prajna, A tutorial on sum of squares techniques for systems analysis, Proc. of the American Control Conference, pp.2686-2700, 2005.
14. A. Papachristodoulou, Scalable Analysis of Nonlinear Systems Using Convex Optimization, Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 2005.
15. S. Prajna, A. Papachristodoulou and P. A. Parrilo, Introducing SOSTOOLS: A general purpose sum of squares programming solver, Proc. of the 41st IEEE Conf. on Decision and Control, vol.1, pp.741-746, 2002.
16. S. Prajna, A. Papachristodoulou and F. Wu, Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach, Proc. of the 5th Asian Control Conference, vol.1, pp.157-165, 2004.
17. B. Samadi and L. Rodrigues, Backstepping controller synthesis for piecewise affine systems: A sum of squares approach, Proc. on ISIC, IEEE International Conf. on System, Man, and Cybernetic, pp.58-63, 2007.
18. J. S. Shamma and M. Athans, Analysis of gain scheduled control for nonlinear plants, IEEE Transactions on Automatic Control, vol.35, no.8, pp.898-907, 1990.
19. T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on System, Man, and Cybernetic, vol.15, pp.116-132, 1985.
20. W. Tan and A. Packard, Stability region analysis using sum of squares programming, Proc. of the American Control Conference, pp.2297-2302, 2006.
21. K. Tanaka, T. Hori and H. O. Wang, A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Transactions on Fuzzy Systems, vol.11, no.4, pp.582-589, 2003.
22. K. Tanaka, T. Ikeda and H. O. Wang, Design of fuzzy control systems based on relaxed LMI stability conditions, Proc. of the IEEE Conf. on Decision and Control, vol.1, pp.598-603, 1996.
23. K. Tanaka, H. Ohtake and H. O. Wang, Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach, IEEE Transactions on Systems, Man, and Cybernetic-part B: Cybernetics, vol.39, no.2, pp.561-567, 2009.
24. K. Tanaka, T. Taniguchi and H. O. Wang, Model-based fuzzy control of TORA system: Fuzzy regulator and fuzzy observer design via LMIs that represent decay rate, disturbance rejection, robustness, optimality, Proc. of 1998 IEEE International Conf. on Fuzzy Systems, vol.1, pp.313-318, 1998.
25. K. Tanaka, H. Yoshida, H. Ohtaka and H. O. Wang, A sum of squares approach to stability analysis of polynomial fuzzy systems, Proc. of 2007 American Control Conference, pp.4071-4076, 2007.
26. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, Stabilization of polynomial fuzzy systems via a sum of squares approach, Proc. of the 22nd IEEE International Symposium on Intelligent Control Part of IEEE Multi-conference on System and Control, pp.160-165, 2007.
27. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems, IEEE Transactions on Fuzzy Systems, vol.17, no.4, pp.911-922, 2009.
28. T. Taniguchi, K. Tanaka and H. O. Wang, Fuzzy descriptor systems and nonlinear model following control, IEEE Transactions on Fuzzy Systems, vol.8, no.4, pp.442-452, 2000.
29. W. J. Wang, Y. J. Chen and C. H. Sun, Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function, IEEE Transactions on Systems, Men, and Cybernetics-Part B: Cybernetics, vol.37, no.3, pp.551-559, 2007.
30. H. O. Wang, K. Tanaka and M. F. Griffin, Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model, Proc. of IEEE International Conference on Fuzzy System, pp.531-538, 1995.
31. D. Wang, W. Wang and X. Wang, Controller failure analysis for T-S fuzzy systems with time-varying delay via a switched approach, International Journal of Innovative Computing, Information and Control, vol.5, no.10, pp.3329-3340, 2009.
32. H. Yang, X. Sun and X. Liu, Stabilization and switched control for a class of switched fuzzy systems, International Journal of Innovative Computing, Information and Control, vol.5, no.10, pp.3099-3108, 2009.
33. Q. Zheng and F. Wu, Improving nonlinear control performance with a hybrid control strategy, Proc. of the 46th IEEE Conf. on Decision and Control, pp.3208-3213, 2007.