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Multiple models with two level adaptation control for a class of nonlinearly parameterized nonlinear system

  • Vinay PandeyEmail author
  • Indrani Kar
  • Chitralekha Mahanta
Article
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Abstract

A multiple models with two level adaptation control method for nonlinearly parameterized nonlinear system is proposed in this article. The proposed adaptive control technique is well suited for controlling nonlinear systems having unknown parameters. An estimation model of the system is designed to tune the unknown parameters. Moreover, the estimation error is shown to converge to zero asymptotically at the first level and the closed loop stability of the overall system after two level is proved using the Lyapunov stability criterion. Furthermore, different configurations for adaptive control using multiple models and selection of the optimum number of models is also reviewed. A cart-pendulum system and an academic example is simulated and results are presented. The improvement in transient and steady state performance as well as better parameter convergence using the proposed scheme are shown as compared to existing single model methods.

Keywords

Multiple model Adaptive control Two level adaptation Nonlinear parameterization Cart-pole system 

References

  1. 1.
    Sastry SS, Isidori A (1989) Adaptive control of linearizable systems. IEEE Trans Autom Control 34(11):1123–1131MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Slotine J-JE, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  3. 3.
    Krstic M, Kanellakopoulos I, Kokotovic PV (1995) Nonlinear and adaptive control design, 1st edn. Adaptive and learning systems for signal processing, communications and control series. Wiley, HobokenzbMATHGoogle Scholar
  4. 4.
    Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
  5. 5.
    Åström KJ, Wittenmark Bjorn (1995) Adaptive control, 2nd edn. Addison-Wesley Longman Publishing Co., Inc., BostonGoogle Scholar
  6. 6.
    Yadav A, Gaur P (2014) AI-based adaptive control and design of autopilot system for nonlinear UAV. Sadhana 39:765–783CrossRefzbMATHGoogle Scholar
  7. 7.
    Shahi M, Manzinan A (2015) Automated adaptive sliding mode control scheme for a class of real complicated systems. Sadhana 40:51–74MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zhang T, Ge S, Hang C, Chai T (2001) Adaptive control of first-order systems with nonlinear parameterization. Int J Adapt Control Signal Process 15:445–470CrossRefGoogle Scholar
  9. 9.
    Lin W, Qian C (2002) Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Trans Autom Control 47:1249–1266MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tyukin I, Prokhorov D, van Leeuwen C (2007) Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization. IEEE Trans Autom Control 52:1543–1559MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hung N, Tuan H, Narikiyo T, Apkarian P (2008) Adaptive control for nonlinearly parameterized uncertainties in robot manipulators. IEEE Trans Control Syst Technol 16:458–468CrossRefGoogle Scholar
  12. 12.
    Ge SS, Hang CC, Zhang T (1999) A direct adaptive controller for dynamic systems with a class of nonlinear parameterizations. Automatica 35(4):741–747MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Guan C, Pan S (2008) Adaptive sliding mode control of electro-hydraulic system with nonlinear unknown parameters. Control Eng Pract 16:1275–1284CrossRefGoogle Scholar
  14. 14.
    Farza M, M’Saad M, Maatoung T, Kamoun M (2009) Adaptive observers for nonlinearly parameterized class of nonlinear systems. Automatica 45:2281–2299MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Boskovic JD (1998) Adaptive control of a class of nonlinearly parameterized plants. IEEE Trans Autom Control 43:930–934MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Loh AP, Annaswamy A, Skantze F (1999) Adaptation in the presence of a general nonlinear parameterization: an error model approach. IEEE Trans Autom Control 44:1634–1652MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Cao C, Annaswamy AM, Kojic A (2003) Parameter convergence in nonlinearly parameterized systems. IEEE Trans Autom Control 48(3):397–412MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Athans, M. and Dunn, K.-P. and Greene, C.S. and Lee, W.H. and Sandell, N.R. and Segall, I. and Willsky, A.S. (1975), The stochastic control of the F-8C aircraft using the multiple model adaptive control (MMAC) method. In: IEEE conference on decision and control including the 14th symposium on adaptive processes, 217–228Google Scholar
  19. 19.
    Narendra KS, Balakrishnan J (1994) Improving transient response of adaptive control systems using multiple models and switching. IEEE Trans Autom Control 39(9):1861–1866MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Narendra KS, Balakrishnan J, Ciliz MK (1995) Adaptation and learning using multiple models, switching, and tuning. Control Syst IEEE 15(3):37–51CrossRefGoogle Scholar
  21. 21.
    Narendra KS, Balakrishnan J (1997) Adaptive control using multiple models. IEEE Trans Autom Control 42(2):171–187MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Narendra KS, Han Z (2011) The changing face of adaptive control: the use of multiple models. Annu Rev Control 35(1):1–12CrossRefGoogle Scholar
  23. 23.
    Han Z, Narendra KS (2012) New concepts in adaptive control using multiple models. IEEE Trans Autom Control 57(1):78–89MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Anderson BDO, Brinsmead T, Liberzon T, Stephen Morse A (2000) Multiple model adaptive control with safe switching. IEEE Trans Autom Control 45:1512–1516CrossRefzbMATHGoogle Scholar
  25. 25.
    Cezayirli A, Ciliz K (2006) Increased transient performance for the adaptive control of feedback linearizable systems using multiple models. Int J Control 79:1205–1215MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Cezayirli A, Ciliz K (2007) Transient performance enhancement of direct adaptive control of nonlinear systems using multiple models and switching. IET Control Theory Appl 1(6):1711–1725CrossRefGoogle Scholar
  27. 27.
    Cezayirli A, Ciliz MK (2008) Indirect adaptive control of non-linear systems using multiple identification models and switching. Int J Control 81(9):1434–1450MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Rosa P, Silvestre C (2014) Multiple-model adaptive control using set-valued observers. Int J Robust Nonlinear Control 24:2490–2511MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Xie J, Yang D, Zhao J (2017) Multiple model adaptive control for switched linear systems: a two-layer switching strategy. Int J Robust Nonlinear Control, [Online].  https://doi.org/10.1002/rnc.4015
  30. 30.
    Chen J, Chen W, Sun J (2017) Smooth controller design for non-linear systems using multiple fixed models. IET Control Theory Appl 11:1467–1473MathSciNetCrossRefGoogle Scholar
  31. 31.
    Teel A, Kadiyala R, Kokotovic P, Sastry S (1990) Indirect techniques for adaptive input output linearization of nonlinear systems. In: American control conference, 79–80Google Scholar
  32. 32.
    Kanellakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Khalil HK (1996) Nonlinear system. Prentice Hall, Englewood CliffsGoogle Scholar
  34. 34.
    Narendra KS, Annaswamy AM (2005) Stable adaptive systems. Dovar Publications, NewYorkzbMATHGoogle Scholar
  35. 35.
    Pandey V, Kar I, Mahanta C (2017) Multiple model adaptive control using second level adaptation for a class of nonlinear systems with linear parameterizations, Int J Dyn Control, [Online].  https://doi.org/10.1007/s40435-017-0374-y

Copyright information

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

Authors and Affiliations

  1. 1.IIT GuwahatiGuwahatiIndia

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