Performance Improvement of Finite Time Parameter Estimation with Relaxed Persistence of Excitation Condition

  • Li Zhao
  • Jianhui ZhiEmail author
  • Ningning Yin
  • Yong Chen
  • Jin Li
  • Jiaolong Liu
Original Article


In this paper, a novel finite time parameter estimation method is proposed to solve the parameter estimation problem for a class of linearly parameterized nonlinear systems. The main feature of the proposed method is that the existing method is modified via concurrent learning technique such that the strict persistence of excitation (PE) condition on the regression matrix is relaxed to a rank condition on the recorded data. This makes the presented method more practical. Furthermore, the convergence rate is improved significantly by sliding mode technique in finite time sense. The simulation results of the existing general nonlinear system illustrate the aforementioned features. Comparison with existing methods from literature proves the effectiveness of the proposed method.


Parameter estimation Finite time Persistence of excitation (PE) Concurrent learning 



This work was supported by National Natural Science Foundation of China under Grant 61304120 and the China Postdoctoral Science Foundation under Grant 2017M613417.


  1. 1.
    Chapellat H, Dahleh M, Bhattacharyya SP (1990) Robust stability under structured and unstructured perturbations. IEEE Trans Autom Control 35(10):1100–1108MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Escobar J, Poznyak A (2015) Benefits of variable structure techniques for parameter estimation in stochastic systems using least squares method and instrumental variables. Int J Adapt Control Signal Process 29(8):1038–1054MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Liu ZT, Li CG (2017) Recursive least squares for censored regression. IEEE Trans Signal Process 65(6):1565–1579MathSciNetCrossRefGoogle Scholar
  4. 4.
    Mao YW, Ding F, Yang EF (2017) Adaptive filteringbased multi-innovation gradient algorithm for input nonlinear systems with autoregressive noise. Int J Adapt Control Signal Process 31(10):1388–1400CrossRefzbMATHGoogle Scholar
  5. 5.
    Ding F, Xu L, Zhu QM (2016) Performance analysis of the generalised projection identification for time-varying systems. IET Control Theory Appl 10(18):2506–2514MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ioannou PA, Sun J (1985) Robust adaptive control. Dover Publications Inc., New YorkzbMATHGoogle Scholar
  7. 7.
    Kulikova MV, Tsyganova JV (2015) Constructing numerically stable Kalman filter-based algorithms for gradient-based adaptive filtering. Int J Adapt Control Signal Process 29(11):1411–1426MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kulikova MV, Tsyganova JV (2016) Finite time control design for bilateral teleoperation system with position synchronization error constrained. IEEE Trans. Cybern 46(3):609–619CrossRefGoogle Scholar
  9. 9.
    Adetola V, Guay M (2008) Finite-time parameter estimation in adaptive control of nonlinear systems. IEEE Trans Autom Control 53(3):807–811MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Adetola V, Guay M (2010) Performance improvement in adaptive control of nonlinear systems. IEEE Trans Autom Control 55(9):2182–2186MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lehrer D, Adetola V, Guay M (2010) Parameter identification methods for non-linear discrete-time systems. In: Proc. 2010 American Control Conference, Baltimore, MD, USA, pp 2170–2175Google Scholar
  12. 12.
    Na J, Mahyuddin MN, Herrmann G, Ren XM (2013) Robust adaptive finite-time parameter estimation for linearly parameterized nonlinear systems. In: Proc. 32nd Chinese Control Conference, Xi’an, China, pp 1735–1741Google Scholar
  13. 13.
    Na J, Yang J, Wu X, Guo Y (2015) Robust adaptive parameter estimation of sinusoidal signals. Automatica 53:376–384MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Na J, Mahyuddin MN, Herrmann G, Ren XM, Barber P (2015) Robust adaptive finite-time parameter estimation and control for robotic systems. Int J Robust Nonlinear Control 25(16):3045–3071MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Adetola V, Guay M (2006) Excitation signal design for parameter convergence in adaptive control of linearizable systems. In: Proc. 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp 447–452Google Scholar
  16. 16.
    Cao CY, Hovakimyan N, Wang J (2007) Intelligent excitation for adaptive control with unknown parameters in reference input. IEEE Trans Autom Control 52(8):1525–1532MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Chowdhary GV, Yucelen T, Mühlegg M, Johnson EN (2013) Concurrent learning adaptive control of linear systems with exponentially convergent bounds. Int J Adapt Control Signal Process 27(4):280–301MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Liao F, Lum KY, Wang JL, Benosman M (2007) Constrained nonlinear finite time control allocation. In: Proc. 2007 American Control Conference, New York, NY, USA, pp 3801–3806Google Scholar
  19. 19.
    Haddad WM, Chellaboina VS (2008) Nonlinear dynamical systems and control: a lyapunov-based approach. Princeton University Press, PrincetonzbMATHGoogle Scholar
  20. 20.
    Chowdhary GV (2010) Concurrent learning for convergence in adaptive control without persistency of excitation, Ph.D. thesis, Atlanta, USA: Aerospace Eng., Georgia TechGoogle Scholar
  21. 21.
    Chowdhary GV, Johnson EN (2011) A singular value maximizing data recording algorithm for concurrent learning. In: Proc. 2011 American Control Conference, San Francisco, CA, USA, pp 3547–3552Google Scholar
  22. 22.
    Zhou FX, Fisher DG (1992) Continuous sliding mode control. Int J Control 55(2):313–327CrossRefzbMATHGoogle Scholar
  23. 23.
    Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Control 43(5):678–682MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Yu SH, Yu XH, Shirinzadeh BJ, Man ZH (2005) Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11):1957–1964MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Krstić M, Kanellakopoulos I, Kokotović P (1995) Nonlinear and adaptive control design. Wiley, New YorkzbMATHGoogle Scholar
  26. 26.
    Huang JT (2003) Sufficient conditions for parameter convergence in linearizable systems. IEEE Trans Autom Control 48(5):878–880MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Lin JS, Kanellakopoulos I (1999) Nonlinearities enhance parameter convergence in strict feedback systems. IEEE Trans Autom Control 44(1):89–94MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Korean Institute of Electrical Engineers 2019

Authors and Affiliations

  • Li Zhao
    • 2
  • Jianhui Zhi
    • 1
    Email author
  • Ningning Yin
    • 3
  • Yong Chen
    • 4
  • Jin Li
    • 5
  • Jiaolong Liu
    • 6
  1. 1.Graduate CollegeAir Force Engineering UniversityXi’anPeople’s Republic of China
  2. 2.Shaanxi Institute of International Trade & CommerceXianyangPeople’s Republic of China
  3. 3.School of Materials Science and Chemical EngineeringXi’an Technological UniversityXi’anPeople’s Republic of China
  4. 4.Aeronautics Engineering CollegeAir Force Engineering UniversityXi’anPeople’s Republic of China
  5. 5.School of Equipment Management and Unmanned Aerial Vehicle EngineeringAir Force Engineering UniversityXi’anPeople’s Republic of China
  6. 6.66133 Unit of PLABeijingPeople’s Republic of China

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