[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Matching localization algorithm of nonlinear T–S fuzzy system constructed by the piecewise linear function

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

The piecewise linear function is a generalization of a segmentation linear functions with one variable in the multivariate case, which is an important tool to describe the relationships between fuzzy system and approximation function. Firstly, aiming at the \({\hat{\mu }}\)-integrable function, the concrete method of constructing piecewise linear functions and their analytical expressions were introduced, furthermore, based on the piecewise linear functions, we constructed the nonlinear T–S fuzzy systems with a singleton fuzzifier in this paper. And then, we put forward the matching-localization algorithm of the fuzzy system based on the spatial positioning mode for the input variables in the domain. Finally, the effectiveness of the matching localization algorithm of the nonlinear T–S fuzzy system was verified by the means of the simulation example. The results show that the approximating ability of the fuzzy system to a \({\hat{\mu }}\)-integrable function can be adjusted by changing the subdivision parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Abdolreza M, Mohammad R (2010) A novel hierarchical clustering combination scheme based on fuzzy similarity relations. IEEE Trans Fuzzy Syst 18(1):27–39

    Article  Google Scholar 

  • Elmazi D, Kulla E, Oda T et al (2015) A comparison study of two fuzzy-based systems for selection of actor node in wireless sensor actor networks. J Ambient Intell Hum Comput 6(5):635–645

    Article  Google Scholar 

  • Hassine R, Karray F, Alimi AM, Selmi M (2003) Approximation properties of fuzzy systems for smooth functions and their first-order derivative. IEEE Trans Syst Man Cybern Part A 33(2):160–168

    Article  Google Scholar 

  • Liu PY, Li HX (2000) Approximation of generalized fuzzy systems to integrable functions. Sci Chin Ser 30(5):413–423

    MathSciNet  Google Scholar 

  • Liu PY, Li HX (2001) Analyses for \(L_{p}(\mu )\)-norm approximation capability of the generalized Mamdani fuzzy Systems. Inf Sci 138(2):95–210

    Google Scholar 

  • Liu FC, Ma LY, Shao J et al (2007) Universal approximation of a class of nonlinear T–S fuzzy system. Autom Instrum 129(1):8–15

    Google Scholar 

  • Li HX, Yuan XH, Wang JY (2010) The normal numbers of the fuzzy systems and their classes. Sci Chin Inf Sci 53(11):2215–2229

    Article  MathSciNet  MATH  Google Scholar 

  • Lin JX, Vazquez S, Wu LG et al (2017) Extended state observer based sliding mode control for three phase power converters. IEEE Trans Ind Electron 64(1):22–31

    Article  Google Scholar 

  • Liu JX, Luo WS, Yang XZ et al (2016) Robust model based fault diagnosis for PEM fuel cell air-feed system. IEEE Trans Ind Electron 63(5):3261–3270

    Article  Google Scholar 

  • Özge U, ürksen IBT (2007) Discrete interval type 2-fuzzy system models using uncertainty in learning parameters. IEEE Trans Fuzzy Syst 15(1):90–106

  • Peng WL (2014) Universal approximation of square piecewise linear functions in \(K\)-integral norms in fuzzy system. J Syst Sci Math Sci 34(3):340–351

    Google Scholar 

  • Ricardo J, Campello GB, Wagner C (2006) Hierarchical fuzzy relational models: linguistic interpretationand universal approximation. IEEE Trans Fuzzy Syst 14(3):446–453

    Article  Google Scholar 

  • Song QK, Zhao ZJ, Yang JX (2013) Passivity and passification for stochastic Takagi–Sugeno fuzzy system with mixed time varying delays. Neurocomputing 122:330–337

    Article  Google Scholar 

  • Takagi T, Sugeno M (1985) Fuzzy identification of system and its applications to modeling and control. IEEE Trans Syst Man Cybern Part A 15(1)1:116–132

  • Tao YJ, Wang HZ, Wang GJ (2015) Approximation and realization of the generalized Mamdani fuzzy system based on \(Kp\)-integral norms induced by K-quasiarithmetic operations. Acta Electron Sin 43(11):2284–2291

    Google Scholar 

  • Vassilis SK, Yannis AP (2009) On the monotonicity of hierarchical sum-product fuzzy systems. Fuzzy Sets Syst 160(24):3530–3538

    Article  MathSciNet  MATH  Google Scholar 

  • Vaccaro A, Zobaa AF (2011) Cooperative fuzzy controllers for autonomous voltage regulation in Smart Grids. J Ambient Intell Hum Comput 2(1):1–10

    Article  Google Scholar 

  • Wang LX (1998) Universal approximation by hierarchical fuzzy systems. Fuzzy Set Syst 93(1):223–230

    Article  MathSciNet  MATH  Google Scholar 

  • Wang LX (1999) Analysis and design of hierarchical fuzzy systems. IEEE Trans Fuzzy Syst 7(5):617–624

    Article  Google Scholar 

  • Wang GJ, Duan CX (2012) Generalized hierarchical hybrid fuzzy systems and their universal approximation. Control Theory Appl 29(5):673–680

    Google Scholar 

  • Wang GJ, Li XP (2011) Universal approximation of polygonal fuzzy neural networks in sense of \(K\)-integral norms. Sci China Inf Sci 54(11):2307–2323

    Article  MathSciNet  MATH  Google Scholar 

  • Wang GJ, Li XP, Sui XL (2014) Universal approximation and its realize process of generalized Mamdani fuzzy system in \(K\)-integral norms. Acta Autom Sin 40(1):143–148

    Google Scholar 

  • Wei YL, Qiu JB, Lam HK et al (2017) Approaches to T-S fuzzy-affine model based reliable output feedback control for nonlinear itô stochastic systems. IEEE Trans Fuzzy Syst 25(3):569–583

    Article  Google Scholar 

  • Wei YL, Qiu JB, Karimi HR (2017) Reliable output feedback control of discrete time fuzzy affine systems with actuator faults. IEEE Trans Circuits Syst I Regul Papers 64(1):170–181

    Article  Google Scholar 

  • Wei YL, Qiu JB, Shi P et al (2016) A new design of H-infinity piecewise filtering for discrete time nonlinear time varying delay systems via T-S fuzzy affine models. IEEE Trans Syst Man Cybern Syst. doi:10.1109/TSMC.2016.2598785

  • Wu LG, Gao YB, Liu JX et al (2017) Event-triggered sliding mode control of stochastic systems via output feedback. Automatica 82:79–92

    Article  MathSciNet  MATH  Google Scholar 

  • Wei YL, Qiu JB, Shi P et al (2017) Fixed order piecewise-affine output feedback contrller for fuzzy-affine model based nonlinear systems with time-varying delay. IEEE Trans Circuits Syst I Regul Papers 64(4):945–958

    Article  Google Scholar 

  • Wei YL, Qiu JB, Lam HK (2016) A novel approach to reliable output feedback control of fuzzy-affine systems with time-delays and sensor faults. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2016. 2633323

  • Wang HZ, Tao YJ, Wang GJ (2015) Approximation analysis of nonhomogeneous linear T–S fuzzy system based on grid piecewise linear function structure. J Syst Sci Math Sci 35(11):1276–1290

    MathSciNet  MATH  Google Scholar 

  • Wang DG, Song WY, Li HX (2015) Approximation properties of ELM-fuzzy systems for smooth functions and their derivatives. Neurocomputing 149:265–274

    Article  Google Scholar 

  • Wang DG, Chen CLP, Song WY, Li HX (2015) Error compensated marginal linearization method for modeling a fuzzy system. IEEE Trans Fuzzy Syst 23(1):215–222

    Article  Google Scholar 

  • Zeng XJ, Madan GG (1994) Singh approximation theory of fuzzy system-SISO case. IEEE Trans Fuzzy Syst 2(2):162–176

  • Zeng XJ, Madan G (1995) Singh Approximation theory of fuzzy system-MIMO case. IIEEE Trans Fuzzy Syst 3(2):219–235

    Article  Google Scholar 

  • Zhang YZ, Li HX (2006) Generalized hierarchical Mamdani fuzzy systems and their universal approximation. Control Theory Appl 23(3):449–454

    MATH  Google Scholar 

  • Zhang GY, Wang GJ (2015) Approximation capability of nonlinear T-S fuzzy system based on triangular fuzzifier to p-integrable functions. J Zhejiang Univ (Science Edition) 42(5):537–541

    MathSciNet  MATH  Google Scholar 

  • Zeng K, Zhang NY, Xu WL (2001) A comparative study on sufficient condition for Takagi–Sugeno fuzzy system as universal approximators. Acta Autom Sin 27(5):606–612

    Google Scholar 

Download references

Acknowledgements

This work has been supported by National Natural Science Foundation China (Grant no. 61374009).

Author information

Authors and Affiliations

  1. School of Mathematics Sciences, Tianjin Normal University, Tianjin, 300387, China

    Guijun Wang & Guoying Zhang

Authors
  1. Guijun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoying Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guijun Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, G., Zhang, G. Matching localization algorithm of nonlinear T–S fuzzy system constructed by the piecewise linear function. J Ambient Intell Human Comput 10, 417–427 (2019). https://doi.org/10.1007/s12652-017-0556-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-017-0556-7

Keywords

Search

Navigation