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A novel identification method for Takagi-Sugeno fuzzy model. (English) Zbl 1400.93319
Summary: Based on the Xie-Beni index and an improved particle swarm optimization algorithm, a novel identification method for the Takagi-Sugeno fuzzy model is proposed in this paper. Firstly, Xie-Beni indices with a fuzzy \(c\)-means clustering algorithm are adopted to find the rule number of the Takagi-Sugeno fuzzy model. By utilizing the particle swarm optimization algorithm, the initial membership function and the consequent parameters of the fuzzy model are obtained. In addition, through an improved fuzzy \(c\)-regression model and orthogonal least-square method, the premise structure and consequent parameters can be obtained to establish the Takagi-Sugeno fuzzy model. Some well-known models are used to demonstrate that the proposed method outperforms some existing methods.
93E12 Identification in stochastic control theory
93C42 Fuzzy control/observation systems
90C59 Approximation methods and heuristics in mathematical programming
90C90 Applications of mathematical programming
93E24 Least squares and related methods for stochastic control systems
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[1] Peng, C.; Fei, M. R., An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay, Fuzzy Sets Syst., 212, 1, 97-109, (2013) · Zbl 1285.93054
[2] Peng, C.; Yue, D.; Fei, M. R., Relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership, IEEE Trans. Fuzzy Syst., 22, 5, 1101-1112, (2014)
[3] Zhang, J.; Peng, C., Event-triggered \(H_\infty\) filtering for networked Takagi-sugeno fuzzy systems with asynchronous constraints, IET Signal Process., 9, 5, 403-411, (2015)
[4] Tsai, S. H., Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input, Int. J. Syst. Sci., 45, 3, 187-201, (2014) · Zbl 1307.93359
[5] Li, C.; Zhou, J.; Kou, B. F.P.; Xiao, J., T-S fuzzy model identification with a gravitational search-based hyperplane clustering algorithm, IEEE Trans. Fuzzy Syst., 20, 2, 305-317, (2012)
[6] Shaker, M. S.; Patton, R., Active sensor fault tolerant output feedback tracking control for wind turbine systems via T-S model, Eng. Appl. Artif. Intell., 34, 1-12, (2014)
[7] Tanaka, K.; Wang, H. O., Fuzzy control systems design and analysis: A linear matrix inequality approach, (2001), Wiley New York
[8] Teixeira, M. C.M.; Żak, S. H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE Trans. Fuzzy Syst., 7, 2, 369-379, (1999)
[9] Tsai, S. H., An improved fuzzy modeling method for a class of multi-input non-affine nonlinear systems, J. Optim. Theory Appl., 157, 1, 287-296, (2013) · Zbl 1264.93135
[10] Kim, E.; Park, M.; Ji, S.; Park, M., A new approach to fuzzy modeling, IEEE Trans. Fuzzy Syst., 5, 3, 328-337, (1997)
[11] Jang, J. S.R.; Sun, C. T.; Mizutani, E., Neuro-fuzzy and soft computing, (1997), Prentice-Hall
[12] Suleman, A., A convex semi-nonnegative matrix factorisation approach to fuzzy c-means clustering, Fuzzy Sets Syst., 270, Jul., 90-110, (2015) · Zbl 1381.62195
[13] Zhang, D.; Ji, M.; Yang, J.; Zhang, Y.; Xie, F., A novel cluster validity index for fuzzy clustering based on bipartite modularity, Fuzzy Sets Syst., 253, 16, 122-137, (2014)
[14] Shahraiyni, H. T.; Sodoudi, S.; Kerschbaumer, A.; Cubasch, U., A new structure identification scheme for ANFIS and its application for the simulation of virtual air pollution monitoring stations in urban areas, Eng. Appl. Artif. Intell., 41, 175-182, (2015)
[15] Hathaway, R. J.; Bezdek, J. C., Switching regression models and fuzzy clustering, IEEE Trans. Fuzzy Syst., 1, 3, 195-204, (1993)
[16] Leski, J. M., ε-insensitive fuzzy c-regression models: introduction to ε-insensitive fuzzy modeling, IEEE Trans. Syst. Man Cybern. B, 34, 1, 4-15, (2004)
[17] Li, C.; Zhou, J.; Xiang, X.; Li, Q.; An, X., T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm, J. Eng. Appl. Artif. Intell., 22, 4-5, 646-653, (2009)
[18] Kang, S. J.; Woo, C. H.; Hwang, H. S.; Woo, K. B., Evolutionary design of fuzzy rule base for nonlinear system modeling and control, IEEE Trans. Fuzzy Syst., 8, 1, 37-45, (2000)
[19] Luo, M.; Sun, F.; Liu, H., Hierarchical structured sparse representation for T-S fuzzy systems identification, IEEE Trans. Fuzzy Syst., 21, 6, 1032-1043, (2013)
[20] Luo, M.; Liu, H.; Sun, F., Joint block structure sparse representation for multi-input-multi-output (MIMO) T-S fuzzy system identification, IEEE Trans. Fuzzy Syst., 22, 6, 1387-1400, (2014)
[21] Kung, C. C.; Su, J. Y., Affine Takagi-sugeno fuzzy modelling algorithm by fuzzy c-regression models clustering with a novel cluster validity criterion, IET Control Theory, 1, 5, 1255-1265, (2007)
[22] Sledge, I. J.; Bezdek, J. C.; Havens, T. C.; Keller, J. M., Relational generalizations of cluster validity indices, IEEE Trans. Fuzzy Syst., 18, 4, 771-786, (2010)
[23] Xie, X. L.; Beni, G., A validity measure for fuzzy clustering, IEEE Trans. Pattern Anal. Mach. Intell., 13, 8, 841-847, (1991)
[24] Han, P.; Shi, J. Z.; Wang, D. F.; Jiao, S. M., FCM clustering algorithm for T-S fuzzy model identification, (Proceedings of the Ninth International Conference on Machine Learning and Cybernetics, vol. 2, Qingdao, (2010)), 563-566
[25] Niazmardi, S.; Homayouni, S.; Safari, A., An improved FCM algorithm based on the SVDD for unsupervised hyperspectral data classification, IEEE J-STARS, 6, 2, 831-839, (2013)
[26] Bezdek, J. C., Pattern recognition with fuzzy objective function algorithms, (1981), Plenum New York · Zbl 0503.68069
[27] Yaghin, R. G.; Ghomi, S. M.T. F.; Torabi, S. A., A possibilistic multiple objective pricing and lot-sizing model with multiple demand classes, Fuzzy Sets Syst., 231, 16, 26-44, (2013) · Zbl 1284.91294
[28] Ko, C. N.; Chang, Y. P.; Wu, C. J., A PSO method with nonlinear time-varying evolution for optimal design of harmonic filters, IEEE Trans. Power Syst., 24, 1, 437-444, (2009)
[29] Sun, T. H.; Tang, C. H.; Tien, F. C., Post-slicing inspection of silicon wafers using the HJ-PSO algorithm under machine vision, IEEE Trans. Semicond. Manuf., 1, 24, 80-88, (2011)
[30] Li, Y. L.; Shao, W.; You, L.; Wang, B. Z., An improved PSO algorithm and its application to UWB antenna design, IEEE Antennas Wirel. Propag. Lett., 12, 1236-1239, (2013)
[31] Shi, R. E. Yu Hui, Particle swarm optimization-based source seeking, IEEE Trans. Autom. Sci. Eng., 12, 3, 865, (2015)
[32] Sugeno, M.; Yasukawa, T., A fuzzy-logic-based approach to qualitative modeling, IEEE Trans. Fuzzy Syst., 1, 1, 7-25, (1993)
[33] Lee, S. J.; Ouyang, C. S., A neuro-fuzzy system modeling with self-constructing rule generation and hybrid SVD-based learning, IEEE Trans. Fuzzy Syst., 11, 3, 341-353, (2003)
[34] Liu, X.; Fang, H.; Chen, Z., A novel cost function based on decomposing least-square support vector machine for Takagi-sugeno fuzzy system identification, IET Control Theory Appl., 8, 5, 338-347, (2014)
[35] Box, G. E.P.; Jenkins, G. M.; Reinsel, G. C., Time series analysis: forecasting and control, (2008), Wiley · Zbl 1154.62062
[36] Lo, J. C.; Yang, C. H., A heuristic error-feedback learning algorithm for fuzzy modeling, IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum., 29, 6, 686-691, (1999)
[37] Wang, L.; Langari, R., Building sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques, IEEE Trans. Fuzzy Syst., 3, 4, 454-458, (1995)
[38] Lin, Y.; Cunningham, G. A., A new approach to fuzzy-neural system modeling, IEEE Trans. Fuzzy Syst., 3, 2, 190-198, (1995)
[39] Rezaee, B.; Zarandi, M. H.F., Data-driven fuzzy modeling for Takagi-sugeno-kang fuzzy system, Inf. Sci., 180, 241-255, (2010)
[40] Kim, E.; Park, M.; Kim, S.; Park, M., A transformed input-domain approach to fuzzy modeling, IEEE Trans. Fuzzy Syst., 6, 4, 596-604, (1998)
[41] Tsekouras, G. E., On the use of the weighted fuzzy c-means in fuzzy modeling, Adv. Eng. Softw., 36, 5, 287-300, (2005) · Zbl 1075.68641
[42] Tsekouras, G. E.; Sarimveis, H.; Kavakli, E.; Bafas, G., A hierarchical fuzzy-clustering approach to fuzzy modeling, Fuzzy Sets Syst., 150, 245-267, (2005) · Zbl 1142.93311
[43] Kim, E.; Lee, H.; Park, M., A simply identified sugeno-type fuzzy model via double clustering, Inf. Sci., 110, 1/2, 25-39, (1998)
[44] Zhua, B.; He, C.-Z.; Panos Liatsis, X.-Y. L., A GMDH-based fuzzy modeling approach for constructing TS model, Fuzzy Sets Syst., 189, 1, 19-29, (2012)
[45] Choi, J.; Oh, S. K.; Pedrycz, W., Identification of fuzzy models using a successive tuning method with a variant identification ratio, Fuzzy Sets Syst., 159, 21, 2873-2889, (2008) · Zbl 1169.93320
[46] Huang, W.; Oh, S. K.; Ding, L.; Kim, H. K.; Joo, S. C., Identification of fuzzy inference systems using a multi-objective space search algorithm and information granulation, J. Electr. Eng., 6, 6, 853-866, (2011)
[47] Jang, J. S.R., ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern., 23, 3, 665-685, (1993)
[48] Sugeno, M.; Kang, G. T., Fuzzy modeling and control of multilayer incinerator, Fuzzy Sets Syst., 18, 3, 329-345, (1986) · Zbl 0612.93022
[49] Sugeno, M.; Kang, G. T., Structure identification of fuzzy model, Fuzzy Sets Syst., 28, 1, 15-33, (1988) · Zbl 0652.93010
[50] Lughofer, E.; Kindermann, S., Sparsefis: data-driven learning of fuzzy systems with sparsity constraints, IEEE Trans. Fuzzy Syst., 18, 2, 396-411, (2010)
[51] Stone, M., Cross-validatory choice and assessment of statistical predictions, J. R. Stat. Soc., 36, 111-147, (1974) · Zbl 0308.62063
[52] Luo, M. N.; Sun, F. C.; Liu, H.; Li, Z. J., A novel T-S fuzzy systems identification with block structured sparse representation, J. Franklin Inst., 351, 7, 3508-3523, (2014) · Zbl 1290.93109
[53] Babuska, R., Fuzzy modeling for control, (1998), Kluwer Academic
[54] Lughofer, E., FLEXFIS: a robust incremental learning approach for evolving TS fuzzy models, IEEE Trans. Fuzzy Syst., 16, 6, 1393-1410, (2008)
[55] Luo, M.; Sun, F.; Liu, H., Dynamic T-S fuzzy systems identification based on sparse regularization, Asian J. Control, 17, 1, 274-283, (2015) · Zbl 1332.93208
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