Output regulation of polynomial-fuzzy-model-based control systems

IEEE Transactions on Fuzzy Systems

Volumn 21, Issue 2, 2013, Pages 262-274

  Lam, H K ^a   Lo, J C ^b  

^a KING'S COLLEGE LONDON   (United Kingdom)

^b NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Output regulation; polynomial fuzzy model based (PFMB) control; stability analysis; sum of squares (SoS)

Indexed keywords

LYAPUNOV STABILITY THEORY; OUTPUT REGULATION; OUTPUT REGULATION PROBLEM; SIMULATION EXAMPLE; STABILITY ANALYSIS; STABILITY AND CONTROL; STABILITY CONDITION; SUM OF SQUARES;

CONTROL SYSTEM SYNTHESIS; CONTROL SYSTEMS; SYSTEM STABILITY; SYSTEMS ENGINEERING;

POLYNOMIALS;

EID: 84875734897     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2012.2211365     Document Type: Article

References (55)

1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modelling and control," IEEE Trans. Syst., Man., Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan. 1985.
2. M. Sugeno and G. T. Kang, "Structure identification of fuzzy model," Fuzzy Sets Syst., vol. 28, no. 1, pp. 15-33, Oct. 1988.
3. G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 5, pp. 676-697, Oct. 2006. (Pubitemid 44607782)
4. 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, Feb. 1996. (Pubitemid 126782417)
5. K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998. (Pubitemid 128750059)
6. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523-534, Oct. 2000.
7. M. C. M. Teixeira, E. Assuncao, and R. G. Avellar, "On relaxed LMIbased designs for fuzzy regulators and fuzzy observers," IEEE Trans. Fuzzy Syst., vol. 11, no. 5, pp. 613-623, Oct. 2003.
8. X. Liu and Q. Zhang, "New approaches to H? controller designs based on fuzzy observers for Takagi-Sugeno fuzzy systems via LMI," Automatica, vol. 39, no. 9, pp. 1571-1582, Sep. 2003.
9. X. Liu and Q. Zhang, "Approaches to quadratic stability conditions and H? control designs for Takagi-Sugeno fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 6, pp. 830-839, Dec. 2003.
10. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, "A new LMIbased approach to relaxed quadratic stabilization of Takagi-Sugeno fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 386-397, Jun. 2006. (Pubitemid 43898881)
11. A. Sala and C. Ariño, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem," Fuzzy Sets Syst., vol. 158, no. 24, pp. 2671-2686, Jul. 2007. (Pubitemid 47513206)
12. J. C. Lo and J. R. Wan, "Studies on linear matrix inequality relaxations for fuzzy control systems via homogeneous polynomials," IET Control Theory Appl., vol. 4, no. 11, pp. 2293-2302, Nov. 2010.
13. S. P. Boyd, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
14. H. K. Lam and F. H. F. Leung, "Stability analysis of fuzzy control systems subject to uncertain grades of membership," IEEE Trans. Syst., Man Cybern, Part B: Cybern., vol. 35, no. 6, pp. 1322-1325, Dec. 2005. (Pubitemid 41800431)
15. H. K. Lam and F. H. F. Leung, "LMI-based stability and performance design of fuzzy control systems: fuzzy models and controllers with different premises," in Proc. Int. Conf. Fuzzy Syst., Vancouver, BC, Canada, 2006, pp. 9499-9506.
16. A. Sala and C. Ariño, "Relaxed stability and performance conditions for Takagi-Sugeno fuzzy systems with knowledge on membership function overlap," IEEE Trans. Syst., Man Cybern, Part B: Cybern., vol. 37, no. 3, pp. 727-732, Jun. 2007. (Pubitemid 46784606)
17. C. Ariño and A. Sala, "Extensions to "stability analysis of fuzzy control systems subject to uncertain grades of membership," IEEE Trans. Syst., Man Cybern, Part B: Cybern., vol. 38, no. 2, pp. 558-563, Apr. 2008. (Pubitemid 351479575)
18. H. K. Lam and M. Narimani, "Stability analysis and performance deign for fuzzy-model-based control system under imperfect premisematching," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 949-961, Aug 2009.
19. A. Sala and C. Ariño, "Relaxed stability and performance LMI conditions for Takagi-Sugeno fuzzy systems with polynomial constraints on membership function shapes," IEEE Trans. Fuzzy Syst., vol. 16, no. 5, pp. 1328-1336, Oct. 2008.
20. A. Kruszewski, A. Sala, T. Guerra, and C. Arino, "A triangulation approach to asymptotically exact conditions for fuzzy summations," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 985-994, Oct. 2009.
21. M. Narimani and H. K. Lam, "Relaxed LMI-based stability conditions for Takagi-Sugeno fuzzy control systems using regional-membershipfunction-shape- dependent analysis approach," IEEE Trans. Fuzzy Syst., vol. 17, no. 5, pp. 1221-1228, Oct. 2009.
22. H. K. Lam and M. Narimani, "Quadratic stability analysis of fuzzy-modelbased control systems using staircase membership functions," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 125-137, Feb. 2010.
23. J. C. Lo and M. L. Lin, "Robust H? nonlinear control via fuzzy static output feedback," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 50, no. 11, pp. 1494-1502, Nov. 2003.
24. H. Li, B. Chen, Q. Zhou, and W. Qian, "Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 39, no. 1, pp. 94-102, Jan. 2009.
25. L. Wu and W. Zheng, "L2-L control of nonlinear fuzzy It̂o stochastic delay systems via dynamic output feedback," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 39, no. 5, pp. 1308-1315, Oct. 2009.
26. H. Gao and T. Chen, "Stabilization of nonlinear systems under variable sampling: a fuzzy control approach," IEEE Trans. Fuzzy Syst., vol. 15, no. 5, pp. 972-983, Oct. 2007. (Pubitemid 47578002)
27. H. Gao, X. Liu, and J. Lam, "Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 39, no. 2, pp. 306-317, Apr. 2009.
28. H. K. Lam, F. H. F. Leung, and P. K. S. Tam, "Fuzzy control of a class of multivariable nonlinear systems subject to parameter uncertainties: model reference approach," Int. J. Approx. Reasoning, vol. 26, no. 2, pp. 129-144, Feb. 2001. (Pubitemid 32196611)
29. H. K. Lam, F. H. F. Leung, and P. K. S. Tam, "A switching controller for uncertain nonlinear systems," IEEE Control Syst. Mag., vol. 22, no. 1, pp. 7-14, Feb. 2002. (Pubitemid 34228790)
30. C. S. Tseng, B. S. Chen, and H. J. Uang, "Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model," IEEE Trans. Fuzzy Syst., vol. 9, no. 3, pp. 381-392, Jun. 2001.
31. M. Wang, B. Chen, X. Liu, and P. Shi, "Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems," Fuzzy Sets Syst., vol. 159, no. 8, pp. 949-967, Apr. 2008.
32. W. J. Wang and L. Luoh, "Stability and stabilization of fuzzy large-scale systems," IEEE Trans. Fuzzy Syst., vol. 12, no. 3, pp. 309-315, Jun. 2004.
33. W. J. Wang and W. W. Lin, "Decentralized PDC for large-scale TS fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 13, no. 6, pp. 779-786, Dec. 2005.
34. W. W. Lin, W. J. Wang, and S. H. Yang, "A novel stabilization criterion for large-scale T-S fuzzy systems," IEEE Trans. Syst.,Man, Cybern., Part B-Cybern., vol. 37, no. 4, pp. 1074-1079, Aug. 2007.
35. J. D. J. Rubio andW. Yu, "A new discrete-time sliding-mode control with time-varying gain and neural identification," Int. J. Control, vol. 79, no. 4, pp. 338-348, Aug. 2006.
36. W. Yu and M. Moreno-Armendariz, "Robust visual servoing of robot manipulators with neuro compensation," J. Franklin Inst., vol. 342, no. 7, pp. 824-838, Nov. 2005. (Pubitemid 41436418)
37. W. Yu and X. Li, "PD control of robot with velocity estimation and uncertainties compensation," Int. J. Robot. Autom., vol. 21, no. 1, pp. 1-9, Jan. 2006. (Pubitemid 43351339)
38. J. H. Ṕerez-Cruz, I. Chairez, A. Poznyak, and J. J. Rubio, "Constrained neural control for the adaptive tracking of power profiles in a TRIGA reactor," Int. J. Innovative Comput., Inform. Control, vol. 7, no. 7(B), pp. 4575-4588, Jul. 2011.
39. 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 Trans. Fuzzy Syst., vol. 17, no. 4, pp. 911-922, Aug. 2009.
40. K. Tanaka, H. Ohtake, and H. O. Wang, "Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach," IEEE Trans. Syst., Man Cybern.-Part B: Cybern., vol. 39, no. 2, pp. 561-567, Apr. 2009.
41. A. Sala and C. Ariño, "Polynomial fuzzy models for nonlinear control: a taylor-series approach," IEEE Trans. Fuzzy Syst., vol. 17, no. 6, pp. 284-295, Dec. 2009.
42. W. Yu and X. Li, "Fuzzy identification using fuzzy neural networks with stable learning algorithms," IEEE Trans. Fuzzy Syst., vol. 12, no. 3, pp. 411-420, Jun. 2004.
43. W. Yu, M. A. Moreno-Armendariz, and F. O. Rodriguez, "System identification using hierarchical fuzzy neural networks with stable learning algorithm," J. Intell. Fuzzy Syst., vol. 18, no. 2, pp. 171-183, Mar. 2007. (Pubitemid 46868435)
44. J. De Jeśus Rubio, "SOFMLS: online self-organizing fuzzy modified leastsquares network," IEEE Trans. Fuzzy Syst., vol. 17, no. 6, pp. 1296-1309, Dec. 2009.
45. J. H. Ṕerez-Cruz, A. Y. Alanis, J. J. Rubio, and J. Pacheco, "System identification using multilayer differential neural networks: A new result," J. Appl. Mathe., vol. 2012, 2012.
46. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, "Nonlinear control synthesis by sum-of-squares optimization: A Lyapunov-based approach," in Proc. Asian Control Conf., Melbourne, Australia, vol. 1, Feb.2004, pp. 157-165. (Pubitemid 40455802)
47. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, "Introducing SOSTOOLS: a general purpose sum of squares programming solver," in Proc. 41st IEEE Conf. Decision Control, vol. 1, Las Vegas, NV, Dec. 2002, pp. 741-746.
48. M. Narimani and H. K. Lam, "SOS-based stability analysis of polynomial fuzzy-model-based control systems via polynomial membership functions," IEEE Trans. Fuzzy Syst., vol. 18, no. 5, pp. 862-871, Oct. 2010.
49. H. K. Lam, "Polynomial fuzzy-model-based control systems: stability analysis via piecewise linear membership functions," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 588-593, Jun. 2011.
50. C. S. Chiu and T. S. Chiang, "Robust output regulation of T-S fuzzy systems with multiple time-varying state and input delays," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 962-975, Aug. 2009.
51. K. Y. Lian, J. J. Liou, and C. Y. Huang, "LMI-based integral fuzzy control of DC-DC converters," IEEE Trans. Fuzzy Systems, vol. 14, no. 1, pp. 71-80, Feb. 2006.
52. H. K. Lam and S. C. Tan, "Stability analysis of fuzzy-model-based control systems: application on regulation of switching DC-DC converter," IET Control Theory Appl., vol. 3, no. 8, pp. 1093-1106, Aug. 2009.
53. J. J. E. Slotine andW. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.
54. W. E. Snyder, Industrial Robots: Computer Interfacing and Control. Englewood Cliffs, NJ: Prentice-Hall, 1985.
55. B. L.Walcott and S. H. Zak, "Combined observer-controller synthesis for uncertain dynamical systems with applications," IEEE Trans. Syst., Man, Cybern., vol. 18, no. 1, pp. 88-104, Jan./Feb. 1988.