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A robust fuzzy adaptive law for evolving control systems

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Abstract

In this paper an adaptive law with leakage is presented. This law can be used in the consequent part of Takagi–Sugeno-based control. The approach enables easy implementation in the control systems with evolving antecedent part. This combination results in a high-performance and robust control of nonlinear and slowly varying systems. It is shown in the paper that the proposed adaptive law is a natural way to cope with the parasitic dynamics. The boundedness of estimated parameters, the tracking error and all the signals in the system is guaranteed if the leakage parameter σ′ is large enough. This means that the proposed adaptive law ensures the global stability of the system. A simulation example is given that illustrates the proposed approach.

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References

  • Angelov P, Filev DP (2004) An approach to online identification of Takagi–Sugeno fuzzy models. IEEE Syst Man Cybern 34(1):484–498

    Google Scholar 

  • Angelov P, Buswell R, Wright JA, Loveday D (2001) Evolving rule-based control. In: EUNITE Symposium, Tenerife (Spain), pp 36–41***

  • 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(3):189–205

    Article  MATH  Google Scholar 

  • Blažič S, Škrjanc I, Matko D (2003) Globally stable direct fuzzy model reference adaptive control. Fuzzy Sets Syst 139(1):3–33

    Article  MATH  Google Scholar 

  • Blažič S, Škrjanc I, Matko D (2010) Adaptive law with a new leakage term. IET Control Theory Appl 4(9):1533–1542

    Article  MathSciNet  Google Scholar 

  • Blažič S, Škrjanc I, Matko D (2012) A new fuzzy adaptive law with leakage. In: 2012 IEEE conference on evolving and adaptive intelligent systems (EAIS), pp 47–50

  • Cara AB, Lendek Z, Babuska R, Pomares H, Rojas I (2010) Online self-organizing adaptive fuzzy controller: application to a nonlinear servo system. In: IEEE international conference on fuzzy systems (FUZZ), pp 1–8. doi:10.1109/FUZZY.2010.5584027

  • Galichet S, Foulloy L (2003) Integrating expert knowledge into industrial control structures. Comput Indus 52(3):235–251

    Article  Google Scholar 

  • Ge S, Wang J (2002) Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans Neural Netw 13(6):1409–1419

    Article  Google Scholar 

  • Ioannou PA, Sun J (1996) Robust adaptive control. Prentice-Hall, Upper Saddle

  • Johanyák ZC, Papp O (2012) A hybrid algorithm for parameter tuning in fuzzy model identification. Acta Polytechnica Hungarica 9(6):153–165

    Google Scholar 

  • Koo KM (2001) Stable adaptive fuzzy controller with time varying dead-zone. Fuzzy Sets Syst 121:161–168

    Article  MATH  MathSciNet  Google Scholar 

  • Krstić M, Kanellakopoulos I, Kokotović P (1995) Nonlinear and Adaptive Control Design. John Wiley and Sons, New York

  • Layne JR, Passino KM (1993) Fuzzy model reference learning control for cargo ship steering. IEEE Control Syst Mag 13:23–34

    Article  Google Scholar 

  • Pomares H, Rojas I, Gonzlez J, Rojas F, Damas M, Fernndez FJ (2002) A two-stage approach to self-learning direct fuzzy controllers. Int J Approx Reason 29(3):267–289

    Article  MATH  Google Scholar 

  • Precup RE, Hellendoorn H (2011) A survey on industrial applications of fuzzy control. Comput Indus 62(3):213–226

    Article  Google Scholar 

  • Precup RE, Preitl S, Faur G (2003) Pi predictive fuzzy controllers for electrical drive speed control: methods and software for stable development. Comput Indus 52(3):253–270

    Article  Google Scholar 

  • Precup RE, David RC, Petriu EM, Preitl S, Rădac MB (2012) Novel adaptive gravitational search algorithm for fuzzy controlled servo systems. IEEE Trans Indus Inform 8(4):791–800

    Article  Google Scholar 

  • Procyk TJ, Mamdani EH (1979) A linguistic self-organizing process controller. Automatica 15:15–30

    Article  MATH  Google Scholar 

  • Rojas I, Pomares H, Gonzalez J, Herrera L, Guillen A, Rojas F, Valenzuela O (2006) Adaptive fuzzy controller: application to the control of the temperature of a dynamic room in real time. Fuzzy Sets Syst 157(16):2241–2258. doi:10.1016/j.fss.2006.03.006

    Google Scholar 

  • Sadeghi-Tehran P, Cara AB, Angelov P, Pomares H, Rojas I, Prieto A (2012) Self-evolving parameter-free rule-based controller. In: IEEE Proceedings of the 2012 World Congress on Computational Intelligence, WCCI-2012, IEEE, pp 754–761

  • Tang Y, Zhang N, Li Y (1999) Stable fuzzy adaptive control for a class of nonlinear systems. Fuzzy Sets Syst 104:279–288

    Article  MATH  MathSciNet  Google Scholar 

  • Tong S, Li Y (2012) Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans Fuzzy Syst 20(1):168–180

    Article  Google Scholar 

  • Tong S, Wang T, Tang JT (2000) Fuzzy adaptive output tracking control of nonlinear systems. Fuzzy Sets Syst 111:169–182

    Article  MATH  MathSciNet  Google Scholar 

  • Vaščák J (2012) Adaptation of fuzzy cognitive maps by migration algorithms. Kybernetes 41(3/4):429–443

    Google Scholar 

  • Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans Neural Netw 3:807–881

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Ljubljana, Faculty of Electrical Engineering, Tržaška 25, 1000, Ljubljana, Slovenia

    Sašo Blažič, Igor Škrjanc & Drago Matko

Authors
  1. Sašo Blažič
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  2. Igor Škrjanc
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  3. Drago Matko
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Correspondence to Sašo Blažič.

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Blažič, S., Škrjanc, I. & Matko, D. A robust fuzzy adaptive law for evolving control systems. Evolving Systems 5, 3–10 (2014). https://doi.org/10.1007/s12530-013-9084-7

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  • DOI: https://doi.org/10.1007/s12530-013-9084-7

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