Skip to main content
SpringerLink
Log in

Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems

  • Published:
Journal of Control Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive neuro-fuzzy control laws are developed using state scaling and backstepping. Semiglobal uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neighborhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. By using fuzzy logic approximation, the proposed control is free of control singularity problem. An adaptive control-based switching strategy is proposed to overcome the uncontrollability problem associated with x 0(t 0) = 0.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Brockett. Asymptotic stability and feedback stabilization[M]// Differential Geometry Control Theory. New York: Birkaeuser, 1983:181–208.

    Google Scholar 

  2. J. Guldner, V. I. Utkin. Stabilization of non-holonomic mobile robots using Lyapunov function for navigation and sliding mode control[C]//Proceedings of the 33rd IEEE Conference on Decision and Control. New York: IEEE, 1994: 2967–2972.

    Google Scholar 

  3. A. Astolfi. Discontinuous control of nonholonomic systems[J]. Systems & Control Letters, 1996, 27(1): 37–45.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Samson. Time-varying feedback stabilization of a nonholonomic wheeled mobile robot[J]. International Journal of Robotics Research, 1993, 12(8): 55–66.

    Google Scholar 

  5. O. J. Sodalen, O. Egeland. Exponential stabilization of nonholonomic chained systems[J]. IEEE Transactions on Automatic Control, 1995, 40(1): 35–49.

    Article  Google Scholar 

  6. I. Kolmanovsky, N. McClamroch. Development in nonholonomic control problems[J]. IEEE Control System Magazine, 1995, 15(6): 20–36.

    Article  Google Scholar 

  7. R. Murray, S. Sastry. Nonholonomic motion planning: Steering using sinusoids[J]. IEEE Transactions on Automatic Control, 1993, 38(5): 700–716.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. MCloskey, R. Murray. Convergence rates for nonholonomic systems in power form[C]//Proceedings of the American Control Conference. Evanston: American Automatic Control Council, 1992: 2489–2493.

    Google Scholar 

  9. W. Huo, S. S. Ge. Exponential stabilization of nonholonomic systems: an ENI approach[J]. International Journal of Control, 2001, 74(15): 1492–1500.

    Article  MATH  MathSciNet  Google Scholar 

  10. S. S. Ge, Z. Sun, T. H. Lee, et al. Feedback linearization and stabilization of second-order nonholonomic chained systems[J]. International Journal of Control, 2001, 74(14): 219–245.

    MathSciNet  Google Scholar 

  11. R. Murray. Control of nonholonomic systems using chained form[J]. Fields Institute Communications, 1993, 1: 219–245.

    Google Scholar 

  12. Z. Sun, S. S. Ge, W. Huo, et al. Stabilization of nonholonomic chained systems via nonregular feedback linearization[J]. Systems & Control Letters, 2001, 44(4): 279–289.

    Article  MATH  MathSciNet  Google Scholar 

  13. Z. Jiang, H. Nijmeijer. A recursive technique for tracking control of nonholonomic systems in chained form[J]. IEEE Transactions on Automatic Control, 1999, 44(2): 265–279.

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Colbaugh, R. Barany, K. Glass. Adaptive control of nonholonomic mechanical systems[C]//Proceedings of the 35th IEEE Conference on Decision and Control. New York: IEEE, 1996: 1428–1434.

    Google Scholar 

  15. J. P. Hespanha, S. Liberzon, A. S. Morse. Towards the supervisory control of uncertain nonholonomic systems[C]//Proceedings of the American Control Conference. Piscataway: IEEE, 1999: 3520–3524.

    Google Scholar 

  16. W. E. Dixon, D. M. Dawson, E. Zergeroglu, et al. Nonlinear Control of Wheeled Mobile Robots[M]. London: Springer-Verlag, 2001.

    Google Scholar 

  17. S. S. Ge, Z. P. Wang, T. H. Lee. Adaptive stabilization of uncertain nonholonomic systems by state and output feedback[J]. Automatica, 2003, 39(8): 1451–1460.

    Article  MATH  MathSciNet  Google Scholar 

  18. Z. Jiang. Robust exponential regulation of nonholonomic systems with uncertainties[J]. Automatica, 2000, 36(2): 189–209.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. S. Ge, C. C. Hang, T. H. Lee, et al. Stable Adaptive Neural Network Control[M]. Boston: Kluwer Academic Publisher, 2002.

    Google Scholar 

  20. A. Yesildirek, F. L. Lewis. Feedback linearization using neural networks[J]. Automatica, 1995, 31(11): 1659–1664.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. B. Kosmatopoulos. Universal stabilization using control lyapunov functions, adaptive derivative feedback, and neural network approximator[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 1998, 28(3): 472–477.

    Article  Google Scholar 

  22. G. A. Rovithakis. Stable adaptive neuro-control design via lyapunov function derivative estimation[J]. Automatica, 2001, 37(8): 1213–1221.

    Article  MATH  MathSciNet  Google Scholar 

  23. R. Fierro, F. L. Lewis. Control of a nonholonomic mobile robot: backstepping kinematics into dynamics[C]//Proceedings of the 34th IEEE Conference on Decision and Control. New York: IEEE, 1995: 3805–3810.

    Google Scholar 

  24. S. S. Ge, T. H. Lee, C. J. Harris. Adaptive Neural Network Control of Robotic Manipulators[M]. London: World Scientific, 1998.

    Google Scholar 

  25. H. Han, C. Su, Y. Stepanenko. Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators[J]. IEEE Transactions on Fuzzy Systems, 2001, 9(2): 315–323.

    Article  Google Scholar 

  26. A. Bloch, S. Drakunov. Stabilization and tracking in the nonholonomic integrator via sliding modes[J]. Systems & Control Letters, 1996, 29(2): 91–99.

    Article  MATH  MathSciNet  Google Scholar 

  27. C. Samson. Control of chained systems: Application to path following and time-varying point-stabilization of mobile robots[J]. IEEE Transactions on Automatic Control, 1995, 40(1): 64–77.

    Article  MATH  MathSciNet  Google Scholar 

  28. G. C. Walsh, L. G. Bushnell. Stabilization of multiple input chained form control systems[J]. Systems & Control Letters, 1995, 25(3): 227–234.

    Article  MATH  MathSciNet  Google Scholar 

  29. A. Bloch, M. Reyhanoglu, N. H. McClamroch. Control and stabilization of nonholonomic dynamic systems[J]. IEEE Transactions on Automatic Control, 1992, 37(11): 1746–1757.

    Article  MATH  MathSciNet  Google Scholar 

  30. O. J. Sørdalen. Conversion of the kinematics of a car with n trailers into a chained form[C]//IEEE International Conference on Robotics and Automation. Los Alamitos: IEEE Computer Society Press, 1993: 382–387.

    Google Scholar 

  31. R. M. Murray. Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems[J]. Mathematics of Control Signals and Systems, 1994, 7(1): 58–75.

    Article  MATH  MathSciNet  Google Scholar 

  32. L. Bushnell, D. Tilbury, S. S. Sastry. Steering three-input chained form nonholonomic systems using sinusoids: The firetruck example[C]//Proceedings of the European Control Conference. Berkeley: University of California, 1993: 1432–1437.

    Google Scholar 

  33. A. Isidori. Nonlinear Control Systems[M]. 3rd ed. Berlin: Springer-Verlag, 1995.

    Google Scholar 

  34. S. S. Ge, C. C. Hang, T. Zhang. Design and performance analysis of a direct adaptive controller for nonlinear systems[J]. Automatica, 1999, 35(11): 1809–1817.

    Article  MATH  MathSciNet  Google Scholar 

  35. L. Jia, S. S. Ge, M.-S. Chiu. Adaptive neuro-fuzzy control of non-affine nonlinear systems[C]//Proceedings of IEEE International Symposium on Intelligent Control. Piscataway: IEEE, 2005: 286–291.

    Google Scholar 

  36. M. Krstić, I. Kanellakopoulos, P. V. Kokotović. Nonlinear and Adaptive Control Design[M]. New York: John Wiley & Sons, 1995.

    Google Scholar 

  37. E. D. Sontag. A ‘universal’ construction of artstein’s theorem on nonlinear stabilization[J]. Systems & Control Letters, 1989, 13(2): 117–123.

    Article  MATH  MathSciNet  Google Scholar 

  38. A. Astolfi, W. Schaufeberger. State and output feedback stabilization of multiple chained systems with discontinuous control[C]// Proceedings of the 35th IEEE Conference on Decision and Control. New York: IEEE, 1996: 1443–1447.

    Google Scholar 

  39. V. I. Arnold. Geometrical Methods in the Theory of Ordinary Differential Equations[M]. Berlin: Springer-Verlag, 1987.

    Google Scholar 

  40. M. M. Polycarpou, P. A. Ioannou. A robust adaptive nonlinear control design[J]. Automatica, 1996, 32(3): 423–427.

    Article  MATH  MathSciNet  Google Scholar 

  41. M. Sampei, T. Tamura, T. Kobayashi, et al. Arbitrary path tracking control of articulated vehicles using nonlinear control theory[J]. International Journal of Robotics Research, 1995, 3(1): 125–131.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Data Storage Institute, A*STAR, 5 Engineering Drive 1 (Off Kent Ridge Crescent, NUS), Singapore, 117608, Singapore

    Fan Hong, Shuzhi Sam Ge, Chee Khiang Pang & Tong Heng Lee

Authors
  1. Fan Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuzhi Sam Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chee Khiang Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tong Heng Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fan Hong.

Additional information

Fan HONG received the Ph.D. degree from the National University of Singapore in 2004. She was with the Department of Electrical & Computer Engineering and the Department of Mechanical Engineering, National University of Singapore, from 2003 to 2005. She is with Data Storage Institute, A*STAR, since 2005 as a senior research fellow. She has been invited to give talks in 2009 JSME-IIP/ASME-ISPS Joint Conference on Micromechatronics for Information and Precision Equipment, Ibaraki, Japan, 2009, and the 7th International Conference on Control and Automation, Christchurch, New Zealand, 2009. Her research interests include adaptive control, robust control, intelligent control of various mechanical-electronic systems, and real-time application and implementation of hard-disk-drive servo systems. She has published more than 40 research papers and one book chapter.

Shuzhi Sam GE received the B.S. degree in Control Engineering from Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China, in 1986 and the Ph.D. degree in Robotics and the Diploma of Imperial College (DIC) from Imperial College of Science, Technology and Medicine, London, U.K., in 1993. He is a founding director of Social Robotics Lab, Interactive Digital Media Institute and a full professor at the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. He has (co)authored three books: Adaptive Neural Network Control of Robotic Manipulators (Singapore: World Scientific, 1998), Stable Adaptive Neural Network Control (Norwell, MA: Kluwer, 2001), and Switched Linear Systems: Control and Design (New York: Springer-Verlag, 2005). He edited a book Autonomous Mobile Robots: Sensing, Control, Decision Making and Applications (New York: Taylor and Francis, 2006), and published over 300 international journal and conference papers. His current research interests include social robotics, multimedia fusion, adaptive control, and intelligent systems.

Dr. Ge has served/been serving as an associate editor for a number of flagship journals, including the IEEE Transactions on Automatic Control, the IEEE Transactions on Control Systems Technology, the IEEE Transactions on Neural Networks, and Automatica. He also serves as an editor of the Taylor & Francis Automation and Control Engineering Series. He serves as vice president of Technical Activities, IEEE Control Systems Society. He provides technical consultation to industrial and government agencies. He is the editor-in-chief of the International Journal of Social Robotics.

Chee Khiang PANG (Justin) was born in Singapore in 1976. He received the B.E. (Hons.), M.E., and Ph.D. degrees in 2001, 2003, and 2007, respectively, all in Electrical and Computer Engineering, from National University of Singapore (NUS), working closely with A*STAR Data Storage Institute (DSI), Singapore. In 2003, he was a visiting fellow in the School of Information Technology and Electrical Engineering (ITEE), University of Queensland (UQ), Brisbane, QLD, Australia, working on probabilistic small signal stability of large-scale interconnected power systems project funded by Electric Power Research Institute (EPRI), Palo Alto, CA, USA. From 2006 to 2008, he was a researcher (tenure) with Central Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo, Japan. In 2007, he was a visiting academic in School of ITEE, UQ, Brisbane, QLD, Australia, and was invited by the IEEE Queensland Section to give a seminar. From 2008 to 2009, he was a visiting research professor in the Automation & Robotics Research Institute, University of Texas at Arlington, TX, USA. Currently, he is an assistant professor in the Department of Electrical and Computer Engineering, National University of Singapore. He is a member of IEEE. In 2008, he was a guest editor for Transactions of the Institute of Measurement and Control. He was an International Program Committee Member for the 2007 IEEE Congress on Evolutionary Computation (CEC). He is a reviewer of many international referred journals and conferences. His current research interests include intelligent diagnosis and prognosis of industrial networked systems, small signal stability analysis for large-scale inter-connected power systems, and precision control of actuators for data storage systems. He has authored more than 40 technical publications, and is currently co-authoring a research monograph by C. K. Pang, F. L. Lewis, T. H. Lee, and Z. Y. Dong, Intelligent Diagnosis and Prognosis of Industrial Networked Systems, in preparation to be submitted to Taylor and Francis Group, CRC Press, December 2010, in this area.

Tong Heng LEE received the B.A. degree with First Class Honors in the Engineering Tripos from Cambridge University, England, in 1980 and the Ph.D. degree from Yale University in 1987. He is a professor in the Department of Electrical and Computer Engineering at the National University of Singapore (NUS), and also a professor in the NUS Graduate School, NUS NGS. He was a past vicepresident (research) of NUS. Dr. Lee’s research interests are in the areas of adaptive systems, knowledge-based control, intelligent mechatronics and computational intelligence. He currently holds associate editor appointments in the IEEE Transactions in Systems, Man and Cybernetics; IEEE Transactions in Industrial Electronics; Control Engineering Practice (an IFAC journal); and the International Journal of Systems Science (Taylor and Francis, London). In addition, he is the deputy editor-in-chief of IFAC Mechatronics journal. Dr. Lee was a recipient of the Cambridge University Charles Baker Prize in Engineering; the 2004 ASCC (Melbourne) Best Industrial Control Application Paper Prize; the 2009 IEEE ICMA Best Paper in Automation Prize; and the 2009 ASCC Best Application Paper Prize. He has also co-authored five research monographs (books), and holds four patents (two of which are in the technology area of adaptive systems, and the other two are in the area of intelligent mechatronics). He has published more than 300 international journal papers. Dr. Lee was an invited panelist at the World Automation Congress, WAC2000, Maui, U.S.A.; an invited keynote speaker for the IEEE International Symposium on Intelligent Control, IEEE ISIC 2003 Houston U.S.A.; an invited keynote speaker for LSMS 2007, Shanghai China; an invited expert panelist for IEEE AIM2009; and an invited plenary speaker for IASTED RTA 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hong, F., Ge, S.S., Pang, C.K. et al. Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems. J. Control Theory Appl. 8, 125–138 (2010). https://doi.org/10.1007/s11768-010-0006-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-010-0006-y

Keywords

Search

Navigation