Skip to main content
SpringerLink
Log in

Asymptotic regulation of cascade systems with unknown control directions and nonlinear parameterization

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

Abstract

A robust partial-state feedback asymptotic regulating control scheme is developed for a class of cascade systems with both nonlinear uncertainties and unknown control directions. A parameter separation technique is introduced to separate the time-varying uncertainty and the unmeasurable state from nonlinear functions. Then, the Nussbaum-type gain method together with the idea of changing supply functions is adopted in the design of a smooth partial-state regulator that can ensure all the signals of the closed-loop system are globally uniformly bounded. Especially, the system state asymptotically converges to zero. The design procedure is illustrated through an example and the simulation results show that the controller is feasible and effective.

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. I. Kanellakopoulos, P. V. Kokotovic, A. S. Morse. Systematic design of adaptive controllers for feedback linearization systems[J]. IEEE Transactions on Automatic Control, 1991, 36(10): 1241–1253.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Adaptive nonlinear control without overparametrization[J]. Systems & Control Letters, 1992, 19(2): 177–185.

    Article  MATH  MathSciNet  Google Scholar 

  3. Z. Jiang, L. Praly. Iterative designs of adaptive controllers with nonlinear integrators[C] //Proceedings of the 30th IEEE Conference on Decision and Control. New York: IEEE Press, 1991: 2482–2487.

    Google Scholar 

  4. R. Marino, P. Tomei. Robust stabilization of feedback linearization time-varying uncertain nonlinear systems[J]. Automatica, 1993, 29(1): 181–189.

    Article  MATH  MathSciNet  Google Scholar 

  5. Z. Qu. Robust control of nonlinear uncertain systems under generalized matching conditions[J]. Automatica, 1993, 29(7): 985–998.

    Article  MATH  Google Scholar 

  6. J. Kaloust, Z. Qu. Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction[J]. IEEE Transactions on Automatic Control, 1995, 40(2): 276–282.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. R. Mudgett, A. S. Morse. Adaptive stabilization of systems with unknown high frequency gain[J]. IEEE Transactions on Automatic Control, 1985, 30(3): 549–554.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Lozano, B. Brogliato. Adaptive control of a simple nonlinear system without a priori information on the plant parameters[J]. IEEE Transactions on Automatic Control, 1992, 37(1): 30–37.

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Brogliato, R. Lozano. Adaptive control of first order nonlinear systems with reduced knowledge of the plant parameters[J]. IEEE Transactions on Automatic Control, 1994, 39(8): 1764–1768.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. D. Nussbaum. Some remarks on the conjecture in parameter adaptive control[J]. Systems & Control Letters, 1983, 3(5): 243–246.

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Martensson. The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization[J]. Systems & Control Letters, 1985, 6(2): 85–91.

    Article  MathSciNet  Google Scholar 

  12. E. P. Ryan. A universal adaptive stabilizer for a class of nonlinear systems[J]. Systems & Control Letters, 1991, 16(4): 209–218.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. P. Ryan. A nonlinear universal servomechanism[J]. IEEE Transactions on Automatic Control, 1994, 39(4): 753–761.

    Article  MATH  Google Scholar 

  14. Z. Ding. Adaptive control of nonlinear systems with unknown virtual control coefficients[J]. International Journal of Adaptive Control and Signal Processing, 2000, 14(4): 505–517.

    Article  MATH  Google Scholar 

  15. X. Ye, J. Jiang. Adaptive nonlinear design without a priori knowledge of control directions[J]. IEEE Transactions on Automatic Control, 1998, 43(11): 1617–1621.

    Article  MATH  MathSciNet  Google Scholar 

  16. S. S. Ge, J. Wang. Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems[J]. IEEE Transactions on Neural Networks, 2002, 13(6): 1409–1419.

    Article  Google Scholar 

  17. X. Ye. Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions[J]. Automatica, 1999, 35(5):929–935.

    Article  MATH  MathSciNet  Google Scholar 

  18. X. Ye. Adaptive nonlinear output-feedback control with unknown high-frequency gain sign[J]. IEEE Transactions on Automatic Control, 2001, 46(1): 112–115.

    Article  MATH  Google Scholar 

  19. S. S. Ge, J. Wang. Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients[J]. IEEE Transactions on Automatic Control, 2003, 48(8): 1463–1469.

    Article  MathSciNet  Google Scholar 

  20. R. Yan, J. Xu. Iterative learning control design without a priori knowledge of the control direction[J]. Automatica, 2004, 40(10):1803–1809.

    Article  MATH  MathSciNet  Google Scholar 

  21. S. S. Ge, F. Hong, T. Lee. Adaptive neural control of nonlinear time-delay system with unknown virtual control coefficients[J]. IEEE Transactions on Systems, Man and Cybernetics-Part B, 2004, 34(1):499–516.

    Article  MathSciNet  Google Scholar 

  22. Z. Jiang, I. Mareels, D. J. Hill, et al. A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS[J]. IEEE Transactions on Automatic Control, 2004, 49(4): 549–562.

    Article  MathSciNet  Google Scholar 

  23. E. Sontag, Y. Wang. On characterizations of the input-to-state stability property[J]. Systems & Control Letters, 1995, 24(5): 351–359.

    Article  MATH  MathSciNet  Google Scholar 

  24. E. Sontag, A. Teel. Changing supply functions in input/state stable systems[J]. IEEE Transactions on Automatic Control, 1995, 40(8):1476–1478.

    Article  MATH  MathSciNet  Google Scholar 

  25. W. Lin, R. Pongvuthithum. Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback[J]. IEEE Transactions on Automatic Control, 2003, 48(10):1809–1816.

    Article  MathSciNet  Google Scholar 

  26. W. Lin, C. Qian. Adding one power integrator: a tool for global stabilizationof high-order cascade nonlinear systems[J]. Systems & Control Letters, 2000, 39(5): 339–351.

    Article  MATH  MathSciNet  Google Scholar 

  27. W. Lin, C. Qian. Adaptive control of nonlinearly parameterized systems: the smooth feedback case[J]. IEEE Transactions on Automatic Control, 2002, 47(8): 1249–1266.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electricity Information and Automation, Qufu Normal University, Rizhao, Shandong, 276826, China

    Qiangde Wang, Chunling Wei & Yuqiang Wu

Authors
  1. Qiangde Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunling Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuqiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiangde Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No.60774010, 60574080) and the research startup Foundation of Qufu Normal University.

Qiangde WANG received his Ph.D. in Control Theory and Control Engineering from Northeastern University. His main research interests include robust control and adaptive control of nonlinear systems.

Chunling WEI received her Ph.D. in Control Theory and Control Engineering from Southeast University. Her research interests include robust control and adaptive control of nonlinear systems.

Yuqiang WU received his Ph.D. in Control Theory and Control Engineering from Southeast University. His main research interests include control of nonlinear system, variable structure control and adaptive control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Q., Wei, C. & Wu, Y. Asymptotic regulation of cascade systems with unknown control directions and nonlinear parameterization. J. Control Theory Appl. 7, 51–56 (2009). https://doi.org/10.1007/s11768-009-6142-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-009-6142-6

Keywords

Search

Navigation