Neural-networks-based Adaptive Control for an Uncertain Nonlinear System with Asymptotic Stability

Article
  • 24 Downloads

Abstract

This paper proposes a neural-networks(NN)-based adaptive controller for an uncertain nonlinear system with asymptotic stability. While the satisfactory performance of the NN-based adaptive controller is validated well in various uncertain nonlinear systems, the stability is commonly restricted to the uniformly ultimate boundedness( UUB). To improve the UUB of the NN-based adaptive control to the asymptotically stability(AS) with continuous control, the existing NN-based adaptive controller is augmented with a robust-integral-signum-error (RISE) feedback term, and overall closed-loop stability is rigorously analyzed by modifying the typical stability analysis for the RISE feedback control. To demonstrate the effectiveness of the proposed controller, numerical simulations for a fault tolerant flight control with a nonlinear F-16 aircraft model are performed.

Keywords

Adaptive control asymptotic stability fault tolerant flight control neural network RISE feedback 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximator,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989. [click]CrossRefMATHGoogle Scholar
  2. [2]
    K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990. [click]CrossRefGoogle Scholar
  3. [3]
    M. M. Polycarpou and P. A. Ioannou, “Identification and control of nonlinear systems using neural networks models: Design and stability analysis,” Univ. Southern California, Los Angeles, CA, Tech. Rep. 91-09-01, 1991.Google Scholar
  4. [4]
    R. Fierro and F. L. Lewis, “Control of nonholonomic mobile robot using neural networks,” IEEE Transactions on Neural Networks, vol. 9, no. 4, pp. 589–600, 1998. [click]CrossRefGoogle Scholar
  5. [5]
    F. Chen and H. Khalil, “Adaptive control of a class of nonlinear discrete-time systems using neural networks,” IEEE Transactions on Automatic Control, vol. 40, no. 5, pp. 791–801, 1995. [click]MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    B. Kim and A. J. Calise, “Nonlinear flight control using neural networks,” AIAA Journal of Guidance, Control, and Dynamics, vol. 20, no. 1, pp. 26–33, 1997. [click]CrossRefMATHGoogle Scholar
  7. [7]
    D. Shin and Y. Kim, “Reconfigurable flight control system design using adaptive neural networks,” IEEE Transactions on Control Systems Technology, vol. 12, no. 1, pp. 87–100, 2004. [click]CrossRefGoogle Scholar
  8. [8]
    S. Yoo, J. Park, and Y. Choi, “Adaptive output feedback control of flexible-joint robots using neural networks: Dynamic surface design approach,” IEEE Transactions on Neural Networks, vol. 19, no. 10, pp. 1712–1726, 2008. [click]CrossRefGoogle Scholar
  9. [9]
    Z. Hou, L. Cheng, and M. Tan, “Decentralized robust adaptive control for the multiagent system consensus problem using neural networks,” IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, vol. 39, no. 3, pp. 636–647, 2009. [click]CrossRefGoogle Scholar
  10. [10]
    H. Li, L. Wang, H. Du, and A. Boulkroune, “Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 3, pp. 642–652, 2017. [click]CrossRefGoogle Scholar
  11. [11]
    L. Wang, H. Li, Q. Zhou, and R. Lu, “Adaptive fuzzy control for nonstrict feedback systems with unmodeled dynamics and fuzzy dead zone via output feedback,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2400–2412, 2017. [click]CrossRefGoogle Scholar
  12. [12]
    Y. Li and S. Tong, “Adaptive neural networks decentralized FTC design for nonstrict-feedback nonlinear interconnected large-scale systems against actuator faults,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2541–2554, 2017. [click]MathSciNetCrossRefGoogle Scholar
  13. [13]
    Y. Li and S. Tong, “Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. PP, no. 99, pp. 1–10. DOI:10.1109/TNNLS.2017.2712698.Google Scholar
  14. [14]
    B. Xian, D. M. Dawson, M. S. de Qeuiroz, and J. Chen, “A continuous asymptotic tracking control strategy for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1206–1211, 2004. [click]MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    J. Shin, J. Huh, and Y. Park, “Asymptotically stable path tracking for lateral motion of an unmanned ground vehicle,” Control Engineering Practice, vol. 40, pp. 102–112, 2015. [click]CrossRefGoogle Scholar
  16. [16]
    P. M. Patre, W. MacKunis, K. Kaiser, and W. E. Dixon, “Asymptotic tracking for uncertain dynamic systems via a multilayer neural network feedforward and RISE feedback control structure,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2180–2185, 2008. [click]MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    P. M. Patre, W. MacKunis, M. Johnson, and W. E. Dixon, “Composite adaptive control for Euler-Lagrange systems with additive disturbances,” Automatica, vol. 46, no. 1, pp. 140–147, 2010.MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    N. Sharma, K. Stegath, C. Gregory, and W. E. Dixon, “Nonlinear neuromuscular electrical stimulation tracking control of a human limb,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 17, no. 6, pp. 576–584, 2009.CrossRefGoogle Scholar
  19. [19]
    J. Shin, H. J. Kim, Y. Kim, and W. E. Dixon, “Asymptotic attitude tracking of the rotorcraft-based UAV via RISE feedback and NN feedforward terms,” Proc. of The 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, pp. 3694–3699, 2010. [click]CrossRefGoogle Scholar
  20. [20]
    J. Shin, H. J. Kim, Y. Kim, and W. E. Dixon, “Autonomous flight of the rotorcraft-based UAV using RISE feedback and NN feedforward terms,” IEEE Transactions on Control System Technology, vol. 20, no. 5, pp. 1392–1399, 2012. [click]CrossRefGoogle Scholar
  21. [21]
    Z. Wilcox, W. MacKunis, S. Bhat, R. Lind, and W. E. Dixon, “Lyapunov-based exponential tracking control of a hypersonic aircraft with aerothermoelastic effects,” Proc. of AIAA Journal of Guidance, Control and Dynamics, vol. 33, no. 4, pp. 1213–1224, 2010. [click]CrossRefGoogle Scholar
  22. [22]
    A. Filippov, “Differential equations with discontinuous right-hand side,” American Mathematical Society Translations, vol. 42, no. 2, pp. 199–231, 1964.MATHGoogle Scholar
  23. [23]
    G. V. Smirnov, Introduction to the Theory of Differential Inclusions, American Mathematical Society, 2002.MATHGoogle Scholar
  24. [24]
    B. Paden and S. Sastry, “A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulator,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 73–82, 1987. [click]MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    H. K. Khalil, Nonlinear Systems, 3rd edition, Prentice-Hall PTR, Upper Saddle River, NJ, 2002.MATHGoogle Scholar
  26. [26]
    W. E. Dixon, A. Behal, D. M. Dawson, and S. P. Nagarkatti, Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach, Birkhauser, Boston, MA, 2003.CrossRefMATHGoogle Scholar
  27. [27]
    E. A. Morelli, “Global nonlinear parametric modeling with application to F-16 aerodynamics,” Proceeding of American Control Conference, pp. 997–1001, 1998. [click]Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.5th R&D Institute 2nd Directorate at Agency for Defense DevelopmentDaejeonKorea
  2. 2.Department of Aerospace EngineeringChungnam National University, 99 Daehakro, Yuseong-guDaejeonKorea
  3. 3.School of Aerospace, Transport and ManufacturingCranfield UniversityCranfield, BedfordshireUK

Personalised recommendations