Joint block structure sparse representation for multi-input-multi-output (MIMO) T-S fuzzy system identification

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 6, 2014, Pages 1387-1400

  Luo, Minnan ^a,b   Sun, Fuchun ^a,b   Liu, Huaping ^a,b  

^a TSINGHUA UNIVERSITY   (China)

^b TSINGHUA NATIONAL LABORATORY FOR INFORMATION SCIENCE AND TECHNOLOGY   (China)

Author keywords

Block structured sparse optimization; fuzzy rule reduction; fuzzy system identification; joint sparse representation

Indexed keywords

EID: 84914178794     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2292973     Document Type: Article

References (62)

1. X. P. Xie, H. J. Ma, Y. Zhao, D. W. Ding, and Y. C. Wang, "Control synthesis of discrete-time T-S fuzzy systems based on a novel non-PDC control scheme," IEEE Trans. Fuzzy Syst., vol. 21, no. 1, pp. 147-157, Feb. 2013.
2. X. J. Li and G. H. Yang, "Switching-type H filter design for T-S Fuzzy systemswith unknown or partially unknown membership functions," IEEE Trans. Fuzzy Syst., vol. 21, no. 2, pp. 385-392, Apr. 2013.
3. R. Babuska, Fuzzy Modeling for Control. Boston, MA, USA: Kluwer, 2001.
4. B. C. Ding, "Dynamic output feedback predictive control for nonlinear systems represented by a Takagi-Sugeno model," IEEE Trans. Fuzzy Syst., vol. 19, no. 5, pp. 831-843, Oct. 2011.
5. M. A. Khanesar, O. Kaynak, andM. Teshnehlab, "Direct model reference Takagi-Sugeno fuzzy control of SISO nonlinear systems," IEEE Trans. Fuzzy Syst., vol. 19, no. 5, pp. 914-924, Oct. 2011.
6. D. Wang, X. J. Zeng, and J. A. Keane, "An evolving construction scheme for fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 18, no. 4, pp. 755-770, Aug. 2010.
7. S. Chiu, "Fuzzy model identification based on cluster estimation," J. Intell. Fuzzy Syst., vol. 2, no. 3, pp. 267-278, 1994.
8. W. Wang and J. Vrbanek, "An evolving fuzzy predictor for industrial applications," IEEE Trans. Fuzzy Syst., vol. 16, no. 6, pp. 1439-1449, Dec. 2008.
9. W. Huang, S. K. Oh, L. Ding, H. K. Kim, and S. C. Joo, "Identification of fuzzy inference systems using a multi-objective space search algorithm and information granulation," J. Electr. Eng., vol. 6, no. 6, pp. 853-866, 2011.
10. J. Choi, S. K. Oh, and W. Pedrycz, "Identification of fuzzy models using a successive tuning method with a variant identification ratio," Fuzzy Sets Syst., vol. 159, no. 21, pp. 2873-2889, 2008.
11. B. Rezaee and M. H. Fazel Zarandi, "Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system," Inform. Sci., vol. 180, pp. 241-255, 2010.
12. C. S. Li, J. Z. Zhou, B. Fu, P. Kou, and J. Xiao, "T-S fuzzy model identification with gravitational search based hyper-plane clustering algorithm," IEEE Trans. Fuzzy Syst., vol. 20, no. 2, pp. 305-317, Apr. 2012.
13. D. Wang, X.J. Zeng, and J.A. Keane, "A structure evolving learning method for fuzzy systems," Evolv. Syst., vol. 1, pp. 83-95, 2010.
14. D. Wang, X. J. Zeng, and J. A. Keane, "An output-constrained clustering approach for the identification of fuzzy systems and fuzzy granular systems," IEEE Trans. Fuzzy Syst., vol. 19, no. 6, pp. 1127-1140, Dec. 2011.
15. D. Wang, X. J. Zeng, and J. A. Keane, "A simplified structure evolving method for Mamdani fuzzy system identification and its application to high-dimensional," Inform. Sci., vol. 220, no. 20, pp. 110-123, 2013.
16. W. Pedrycz, "Linguistic models as a framework of user-centric system modeling," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 36, no. 4, pp. 727-745, Jul. 2006.
17. J. Abonyi, R. Babusska, and F Szeifert, "Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 32, no. 5, pp. 612-621, Oct. 2002.
18. J. Yen and L.Wang, "Simplifying fuzzy rule-based models using orthogonal transformation methods," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 29, no. 1, pp. 13-24, Feb. 1999.
19. S. Jakubek, C. Hametner, and N. Keuth, "Total least squares in fuzzy system identification: An application to an industrial engine," Eng. Appl. Artif. Intell., vol. 21, no. 8, pp. 1277-1288, 2008.
20. L. X. Wang and J. M. Mendel, "Fuzzy basis functions, universal approximation and orthogonal least-squares learning," IEEE Trans. Neural Netw., vol. 3, no. 5, pp. 807-814, Sep. 1992.
21. S. Destercke, S. Guillaume, and B. Charnomordic, "Building an interpretable fuzzy rule base from data using orthogonal least squares application to a depollution problem," Fuzzy Sets Syst., vol. 158, no. 18, pp. 2078-2094, 2007.
22. L. X.Wang and R. Langari, "Building Sugeno-type model using fuzzy discretization and orthogonal parameter estimation techniques," IEEE Trans. Fuzzy Syst., vol. 3, no. 4, pp. 454-458, Nov. 1995.
23. Y. Yam, P. Baranyi, and C. T. Yang, "Reduction of fuzzy rule base via singular value decomposition," IEEE Trans. Fuzzy Syst., vol. 7, no. 2, pp. 120-131, Apr. 1999.
24. P. Baranyi, Y. Yam, A. Varkonyi-Koczy, and R. J Patton, "SVD based reduction toMISO TS fuzzy models," IEEE Trans. Ind. Electron., vol. 50, no. 1, pp. 232-242, Feb. 2003.
25. P. Baranyi and A. R. Varkonyi Koczy, "Adaptation of SVD based fuzzy reduction via minimal expansion," IEEE Trans. Instrum. Meas., vol. 51, no. 2, pp. 222-226, Apr. 2002.
26. P. Baranyi, Y. Yam, A. R. Varkonyi Koczy, R. J Patton, P. Michelberger, andM. Sugiyama, "SVDbased complexity reduction to TS fuzzy models," IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 433-443, Apr. 2002.
27. P. Baranyi, Y. Yam, C. T. Yang, P. Varlaki, and P Michelberger, "Inference algorithm independent SVD fuzzy rule base complexity reduction," Int. J. Adv. Comput. Intell., vol. 5, no. 1, pp. 22-30, 2001.
28. P. Baranyi, A. R. Varkonyi Koczy, Y Yam, and R. J. Patton, "Adaption of TS Fuzzy Models without Complexity Expansion: HOSVD based approach," IEEE Trans. Instrum. Meas., vol. 54, no. 1, pp. 52-60, Feb. 2005.
29. P. Baranyi, Y. Yam, and P. Varlaki, Tensor Product Model Transformation in Polytopic Model-Based Control. Boca Raton, FL, USA: Taylor and Francis, 2013, p. 240.
30. P. Baranyi, "The generalized TP model transformation for TS fuzzy model manipulation and generalized stability verification," IEEE Trans. Fuzzy Syst., DOI 10.1109/TFUZZ.2013.2278982.
31. P. Baranyi, "TP model transformation as a way to LMI based controller design," IEEE Trans. Ind. Electron., vol. 51, no. 2, pp. 387-400, Apr. 2004.
32. P. Baranyi and Y. Yam, "Case study of the TP model transformation in the control design of a complex dynamic model with structural non-linearity," IEEE Trans. Ind. Electron., vol. 53. no. 3, pp. 895-904, Jun. 2006.
33. P. Baranyi, D. Tikk, Y. Yam, and R. J. Patton, "From differential equations to PDC controller design via numerical transformation," Comput. Ind., vol. 51, pp. 281-297, 2003.
34. D. Tikk, P Baranyi, and R. J Patton, "Approximation properties of TP model forms and its consequents to TPDC design framework," Asian J. Control, vol. 9, no. 3, pp. 221-231, 2007.
35. Y. Yamand L. T. Koczy, "Representingmembership functions as points in high-dimensional spaces for fuzzy interpolation and extrapolation," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 761-772, Dec. 2000.
36. K. W.Wong, D. Tikk, T. D. Gedeon, and L. T. Koczy, "fuzzy rule interpolation for multidimensional input spaces with applications: A case study," IEEE Trans. Fuzzy Syst., vol. 13, no. 6, pp. 809-819, Dec. 2005.
37. L. T. Koczy and K Hirota, "Rule interpolation by level sets in fuzzy approximate reasoning," Bull. Stud. Exchanges Fuzziness Appl., vol. 46, pp. 115-123, 1991.
38. P. Baranyi, L. T. Koczy, and T. D Gedeon, "A generalized concept for fuzzy rule interpolation," IEEE Trans. Fuzzy Syst., vol. 12, no. 6, pp. 820-832, Dec. 2004.
39. D. Tikk and P. Baranyi,"Comprehensive analysis of a new fuzzy rule interpolation method," IEEE Trans. Fuzzy Syst., vol. 8, no. 3, pp. 281-296, Jun. 2000.
40. E. Lughofer and S.Kindermann, "SparseFIS: data-driven learning of fuzzy systems with sparsity constraints," IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 396-411, Apr. 2010.
41. M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. NewYork, NY, USA: Springer-Verlag, 2010.
42. M. N. Luo, F. C. Sun, and H. P. Liu, "Hierarchical structured sparse representation for T-S fuzzy systems identification," IEEE Trans. Fuzzy Syst., vol. 21, no. 6, pp. 1032-1043, Nov. 2013.
43. S. GHaribshaiyan and K. Salahshoor, "Application of an adaptive Takagi-Sugeno fuzzy identification approach for interaction analysis of MIMO nonlinear systems," in Proc. IEEE Int. Conf. Comput.-Aided Control Syst., 2008, pp. 359-364.
44. P. Angelov, C. Xydeas, and D. Filev, "On-line identification of MIMO evolving Takagi-Sugeno fuzzy models," in Proc. IEEE Int. Conf. Fuzzy Syst., 2004, vol. 1, pp. 55-60.
45. X. J. Zeng and M. G. Singh, "Approximation theory of fuzzy systems-MIMO case," IEEE Trans. Fuzzy Syst., vol. 3, no. 2, pp. 219-235, May 1995.
46. L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ, USA: Prentice-Hall, 1994.
47. J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Simultaneous sparse approximation via Greedy pursuit," presented at the Int. Conf. Acoustics, Speech, Signal Process., Philadelphia, PA, USA, Mar. 2005.
48. J. A. Tropp, A. C. Gilbert, andM. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process. (Special Issue Sparse Approx. Signal Image Process.), vol. 86, pp. 572-588, 2006.
49. J. A. Tropp, "Algorithms for simultaneous sparse approximation. Part II: Convex relaxation," Signal Process. (Special Issue Sparse Approx. Signal Image Process.), vol. 86, pp. 589-602, 2006.
50. J. Chen and X. Huo, "Theoretical results on sparse representations of multiple-measurement vectors," IEEE Trans. Signal Process., vol. 54, no. 12, pp. 4634-4643, Dec. 2006.
51. S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Process., vol. 53, no. 7, pp. 2477-2488, Jul. 2005.
52. I. F. Gorodnitsky, J. S. George, and B. D. Rao, "Neuromagnetic source imaging with FOCUSS: A recursive weighted minimum norm algorithm," Electroencephalogr. Clin. Neurophysiol., vol. 95, no. 4, 1995.
53. M. Yuan and Y. Lin, "Model selection and estimation in regression with grouped variables," J. Roy. Statist. Soc. B, vol. 68, no. 1, 2006.
54. A. C. Lozano, G. Swirszcz, N. Abe, "Grouped orthogonal matching pursuit for variable selection and prediction," presented at the Neural Inf. Process. Syst., New York, NY, USA, 2009.
55. M. E. Davies and Y. C. Eldar, "Rank awareness in joint sparse recovery," IEEE Trans. Inform. Theory, vol. 58, no. 2, pp. 1135-1146, Feb. 2012.
56. Y. C. Eldar, P. Kuppinger, and H. Bolcskei, "Block-Sparse signals: Uncertainty relations and efficient recovery," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3042-3054, Jun. 2010.
57. J. C. Bezdek, Pattern Recognition With Fuzzy Objective Function Algorithms. Boston, MA, USA: Kluwer, 1981.
58. E. Lughofer, "Extensions of vector quantization for incremental clustering," Pattern Recog., vol. 41, no. 3, pp. 995-1011, 2008.
59. D. Dovzan and I. Skrjanc, "Recursive clustering based on a Gustafson-Kessel algorithm," Evolv. Syst., vol. 2, no. 1, pp. 15-24, 2011.
60. P. Angelov, "Evolving Takagi-Sugeno fuzzy systems from streaming data (eTs+)," in Evolving Intelligent Systems: Methodology Applications. Hoboken, NJ, USA: Wiley, 2010.
61. R. Kohavi, "A study of cross-validation and bootstrap for accuracy estimation and model selection," in Proc. Int. Joint Conf. Artif. Intell., 1995, vol. 2, no. 12, pp. 1137-1145.
62. J. S. R. Jang, "ANFIS: Adaptive-network-based fuzzy inference systems," IEEE Trans. Syst., Man Cybern., vol. 23, no. 3, pp. 665-685, May 1993.