Online non-affine nonlinear system identification based on state-space neuro-fuzzy models

  • P. GilEmail author
  • T. Oliveira
  • L. Brito Palma
Methodologies and Application


This paper proposes a new general recurrent state-space neuro-fuzzy model structure. Three topologies are under assessment, including the state-input recurrent neuro-fuzzy system, the series-parallel recurrent neuro-fuzzy system and the parallel recurrent neuro-fuzzy system. Moreover, the underlying generalised state-space Takagi–Sugeno system is proven to be a universal approximator, and some stability conditions derived for this system. The online training is carried out based on a constrained unscented Kalman filter, where weights, membership functions and consequents are recursively updated. Results from experiments on a benchmark MIMO system demonstrate the applicability and flexibility of the proposed system identification approach.


Nonlinear system identification Takagi–Sugeno models Neuro-fuzzy systems Unscented transform Kalman filter 


Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflicts of interest.

Ethical approval

This article does no contain any studies with human participants or animals performed by any of the authors.


  1. Ariño C, Sala A, Pérez E, Bedate F, Querol A (2017) Asymptotically exact stabilisation for constrained discrete Takagi–Sugeno systems via set-invariance. Fuzzy Sets Syst 316:117–138 (theme: control engineering)Google Scholar
  2. Bourahala F, Guelton K, Manamanni N, Khaber F (2016) Relaxed controller design conditions for Takagi–Sugeno systems with state time-varying delays. Int J Fuzzy Syst 1–11Google Scholar
  3. Chang Y-C, Chen C-H, Zhu Z-C, Huang Y-W (2016a) Speed control of the surface-mounted permanent-magnet synchronous motor based on Takagi–Sugeno fuzzy models. IEEE Trans Power Electron 31(9):6504–6510CrossRefGoogle Scholar
  4. Chang P-C, Wu J-L, Lin J-J (2016b) A Takagi–Sugeno fuzzy model combined with a support vector regression for stock trading forecasting. Appl Soft Comput 38:831–842CrossRefGoogle Scholar
  5. Dash R, Dash PK (2016) Efficient stock price prediction using a self evolving recurrent neuro-fuzzy inference system optimized through a modified technique. Exp Syst Appl 52:75–90CrossRefGoogle Scholar
  6. Dunik J, Simandl M, Straka O (2012) Unscented Kalman filter: aspects and adaptive setting of scaling parameter. IEEE Trans Autom Control 57(9):2411–2416MathSciNetCrossRefzbMATHGoogle Scholar
  7. Feng G (2006) A survey on analysis and design of model-based fuzzy control systems. IEEE Trans Fuzzy Syst 14(5):676–697MathSciNetCrossRefGoogle Scholar
  8. Feng Z, Zheng WX (2017) Improved stability condition for Takagi–Sugeno fuzzy systems with time-varying delay. IEEE Trans. Cybern. 47(3):661–670CrossRefGoogle Scholar
  9. Gao Q (2017) Universal fuzzy models and universal fuzzy controllers for stochastic non-affine nonlinear systems. In: Universal fuzzy controllers for non-affine nonlinear systems. Springer, Singapore, pp 45–70Google Scholar
  10. Gao Q, Zeng X-J, Feng G, Wang Y, Qiu J (2012) T–S-fuzzy-model-based approximation and controller design for general nonlinear systems. IEEE Trans Syst Man Cybern B Cybern 42(4):1143–1154CrossRefGoogle Scholar
  11. Gao Q, Feng G, Dong D, Liu L (2015) Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems. IEEE Trans Cybern 45(5):880–887CrossRefGoogle Scholar
  12. Husek P (2016) On monotonicity of Takagi–Sugeno fuzzy systems with ellipsoidal regions. IEEE Trans Fuzzy Syst 24(6):1673–1678CrossRefGoogle Scholar
  13. Li L, Yu D, Xia Y, Yang H (2017) Stochastic stability of a modified unscented Kalman filter with stochastic nonlinearities and multiple fading measurements. J Franklin Inst 354(2):650–667MathSciNetCrossRefzbMATHGoogle Scholar
  14. Liu Y, Lee S (2016) Stability and stabilization of Takagi–Sugeno fuzzy systems via sampled-data and state quantized controller. IEEE Trans Fuzzy Syst 24(3):635–644Google Scholar
  15. Lin G, Zhao K, Wan Q (2016) Takagi–Sugeno fuzzy model identification using coevolution particle swarm optimization with multi-strategy. Appl Intell 1–11Google Scholar
  16. Maree J, Imsland L, Jouffroy J (2016) On convergence of the unscented Kalman–Bucy filter using contraction theory. Int J Syst Sci 47(8):1816–1827MathSciNetCrossRefzbMATHGoogle Scholar
  17. Pak JM, Ahn CK, Lee CJ, Shi P, Lim MT, Song MK (2016) Fuzzy horizon group shift fir filtering for nonlinear systems with Takagi–Sugeno model. Neurocomputing 174:1013–1020CrossRefGoogle Scholar
  18. Robles R, Sala A, Bernal M, Gonzalez T (2017) Subspace-based Takagi–Sugeno modeling for improved LMI performance. IEEE Trans Fuzzy Syst 25:754–767CrossRefGoogle Scholar
  19. Scardua LA, da Cruz JJ (2017) Complete offline tuning of the unscented Kalman filter. Automatica 80:54–61MathSciNetCrossRefzbMATHGoogle Scholar
  20. Shi K, Wang B, Yang L, Jian S, Bi J (2017) Takagi–Sugeno fuzzy generalized predictive control for a class of nonlinear systems. Nonlinear Dyn 1–9Google Scholar
  21. Siminski K (2017) Interval type-2 neuro-fuzzy system with implication-based inference mechanism. Exp Syst Appl 79:140–152CrossRefGoogle Scholar
  22. Teixeira B, Tôrres L, Aguirre L, Bernstein D (2010) On unscented Kalman filtering with state interval constraints. J Process Control 20(1):45–57CrossRefGoogle Scholar
  23. Xu S, Sun G, Sun W (2017) Takagi–Sugeno fuzzy model based robust dissipative control for uncertain flexible spacecraft with saturated time-delay input. ISA Trans 66:105–121CrossRefGoogle Scholar
  24. Zeng X-J, Singh MG (1995) Approximation theory of fuzzy systems-mimo case. Trans Fuzzy Syst 3(2):219–235CrossRefGoogle Scholar
  25. Zhu K, Gonska H (2008) Eigenvalue constraints for the stability of TS fuzzy models. In: 2008 American control conference, vol 88. Taylor & Francis, SeattleGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre of Technology and Systems (CTS)-UNINOVAMonte de CaparicaPortugal
  2. 2.Electrical Engineering Department, Faculty of Science and TechnologyUniversidade NOVA de LisboaMonte de CaparicaPortugal
  3. 3.CISUC - Centre for Informatics and Systems of the University of CoimbraUniversidade de CoimbraCoimbraPortugal

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