Abstract
An approach for investigating controllability and observability properties in Takagi-Sugeno (TS) fuzzy systems is given. The proposed method is independent of the number of fuzzy rules acting at the same instant and independent of the number of inputs and outputs included in the TS fuzzy model. Therefore, it can be applied to a wide class of fuzzy systems. The analysis relies on the solution of a set of symbolic simultaneous equations with the fuzzy weights as the unknowns of such equations.
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References
Angelov P, Kasabov NK (2005) Evolving computational intelligence systems. In: Proceedings of the 1st international workshop on genetic fuzzy systems, pp 76–82
Angelov P, Yager R (2013) Density-based averaging—a new operator for data fusion. Inf Sci 222:163–174 (Including Special Section on New Trends in Ambient Intelligence and Bio-inspired Systems)
Angelov P, Victor J, Dourado A, Filev D (2004) On-line evolution of Takagi-Sugeno fuzzy models. In: 2nd IFAC Workshop on Advanced Fuzzy/Neural Control (AFNC04) IFAC Proceedings vol 37, no (16), Oulu, Finland, September, 16-17, pp 67–72
Angelov P, Filev D, Kasabov N (2010) Evolving intelligent systems-methodology and applications. Wiley, New York
Angelov P, Sadeghi-Tehran P, Ramezani R (2011) An approach to automatic real-time novelty detection, object identification, and tracking in video streams based on recursive density estimation and evolving Takagi-Sugeno fuzzy systems. Int J Intell Syst 26:189–205
Angelov P, Skrjanc I, Blazic S (2015) A robust evolving cloud-based controller. In: Kacprzyk J, Pedrycz W (eds) Springer handbook of computational Intelligence. Springer, pp 1435–1449
Baruah RD, Angelov P (2012) Evolving local means method for clustering of streaming data. In: 2012 IEEE International Conference on Fuzzy Systems, pp 1–8
Baruah RD, Angelov P (2014) Dynamically evolving clustering and its application to structure identification of evolving fuzzy models. IEEE Trans Cybern 44(9):1619–1631
Kailath T (1980) Linear systems. Prentice-Hall Inc, Upper Saddle River
Khalil HK (1996) Nonlinear systems. Prentice Hall, Upper Saddle River
Lee HC, Choi JW (2005) Ackermann-like eigenvalues assigment formulae for linear time-varying systems. IEE Proc Control Theory Appl 152(4):427–434
Leite D, Palhares RM, Campos VCS, Gomide F (2015) Evolving granular fuzzy model-based control of nonlinear dynamic systems. IEEE Trans Fuzzy Syst 23(4):923–938
Meda-Campana JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968–31973
Meda-Campana JA, Gomez-Mancilla JC, Castillo-Toledo B (2012) Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 20(2):235–247
Meda-Campana JA, Rodriguez-Valdez J, Hernandez-Cortes T, Tapia-Herrera R, Nosov V (2015) Analysis of the fuzzy controllability property and stabilization for a class of t-s fuzzy models. IEEE Trans Fuzzy Syst 23(2):291–301
Meda-Campana JA, Araceli G, Rubio JJ, Tapia-Herrera R, Hernandez-Cortes T, Curtidor-Lopez AV, Paramo-Carranza LA, Cazares-Ramirez IO (2018) Design of stabilizers and observers for a class of multivariable ts fuzzy models on the basis of new interpolation functions. IEEE Trans Fuzzy Syst 26(5):2649–2662
Mota VC, Damasceno FA, Leite DF (2018) Fuzzy clustering and fuzzy validity measures for knowledge discovery and decision making in agricultural engineering. Comput Electron Agric 150:118–124
Palm R, Driankov D, Hellendoorn H (1997) Model based fuzzy control: fuzzy gain schedulers and sliding mode fuzzy controllers. Springer, Berlin
Precup R-E, Tomescu ML, Radac M-B, Petriu EM, Preitl S, Dragos C-A (2012) Iterative performance improvement of fuzzy control systems for three tank systems. Expert Syst Appl 39:8288–8299
Precup R-E, Filip H-I, Radac M-B, Petriu EM, Preitl S, Dragos C-A (2014) Online identification of evolving Takagi-Sugeno-Kang fuzzy modelsfor crane systems. Appl Soft Comput 24:1155–1163
Skogestad S, Postlethwaite I (2005) Multivariable feedback control, analisis and design. Wiley, New York
Tanaka K, Sugeno M (1992) Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst 45(2):135–156
Tanaka K, Wang HO (2001) Fuzzy control systems design and analysis. A linear matrix inequality approach. Wiley, New York
Tsalakis KS, Ioannou PA (1993) Linear time-varying systems, control and adaptation. Prentice Hall, Englewwod Cliffs
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Authors are grateful with the Editor-in-Chief, Associate Editor, and Reviewers for their valuable comments and insightful suggestions, which helped to improve this research significantly. Authors thank the Instituto Politécnico Nacional, the Secretaría de Investigación y Posgrado, the Comisión de Operación y Fomento de Actividades Académicas, and the Consejo Nacional de Ciencia y Tecnología for their help in this research.
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Meda-Campaña, J.A., de J. Rubio, J., Aguilar-Ibañez, C. et al. General controllability and observability tests for Takagi-Sugeno fuzzy systems. Evolving Systems 11, 349–358 (2020). https://doi.org/10.1007/s12530-019-09281-w
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DOI: https://doi.org/10.1007/s12530-019-09281-w