Skip to main content
SpringerLink
Log in

Robust control design for a class of mismatched uncertain nonlinear systems

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.

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. Corless, M.,Control of Uncertain Nonlinear Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 362–372, 1993.

    Google Scholar 

  2. Leitmann, G.,On One Approach to the Control of Uncertain Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 373–380, 1993.

    Google Scholar 

  3. Leitmann, G.,On the Efficacy of Nonlinear Control in Uncertain Linear Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 103, pp. 95–102, 1981.

    Google Scholar 

  4. Corless, M. J., andLeitmann, G.,Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 1139–1144, 1981.

    Article  Google Scholar 

  5. Barmish, B. R., Corless, M., andLeitmann, T.,A New Class of Stabilizing Controllers for Uncertain Dynamical Systems, SIAM Journal on Control and Optimization, Vol. 21, pp. 246–255, 1983.

    Article  Google Scholar 

  6. Barmish, B. R., andLeitmann, G.,On Ultimate Boundedness Control of Uncertain Systems in the Absence of Matching Conditions, IEEE Transactions on Automatic Control, Vol. 27, pp. 153–157, 1982.

    Article  Google Scholar 

  7. Chen, Y. H.,On the Robustness of Mismatched Uncertain Dynamical Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 109, pp. 29–35, 1987.

    Google Scholar 

  8. Chen, Y. H., andLeitmann, G.,Robustness of Uncertain Systems in the Absence of Matching Assumptions, International Journal of Control, Vol. 45, pp. 1527–1542, 1987.

    Google Scholar 

  9. Swei, S. M., andCorless, M.,On the Necessity of the Matching Condition in Robust Stabilization, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, pp. 2611–2614, 1991.

  10. Petersen, I. R., Corless, M., andRyan, E. P.,A Necessary and Sufficient Condition for Quadratic Finite-Time Feedback Controllability, Proceedings of the International Workshop on Robust Control, Ascona, Switzerland, pp. 265–269, 1992.

  11. Chao, C. H., andStalford, H. L.,On the Robustness of Linear Stabilizing Feedback Control for Linear Uncertain Systems: Multi-Input Case, Journal of Optimization Theory and Applications, Vol. 64, pp. 229–244, 1990.

    Article  Google Scholar 

  12. Petersen, I. R., andHollot, C. V.,A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems, Automatica, Vol. 22, pp. 397–411, 1986.

    Article  Google Scholar 

  13. Barmish, B. R.,Necessary and Sufficient Conditions for Quadratic Stabilizability of an Uncertain System, Journal of Optimization Theory and Applications, Vol. 46, pp. 399–408, 1985.

    Article  Google Scholar 

  14. Gu, K., Chen, Y. H., Zhody, M. A., andLoh, N. K.,Quadratic Stabilizability of Uncertain Systems: A Two-Level Optimization Setup, Automatica, Vol. 27, pp. 161–165, 1991.

    Article  Google Scholar 

  15. Singh, S. N., andCoelho, A. A. R.,Ultimate Boundedness Control of Set Points of Mismatched Uncertain Systems, International Journal of Systems Science, Vol. 14, pp. 693–710, 1983.

    Google Scholar 

  16. Chen, Y. H.,A New Matching Condition for Robust Control Design, Proceedings of the 1993 American Control Conference, San Francisco, California, pp. 122–126, 1993.

  17. Marino, R., andTomei, P.,Robust Stabilization of Feedback Linearizable Time-Varying Uncertain Nonlinear Systems, Automatica, Vol. 29, pp. 181–189, 1993.

    Article  Google Scholar 

  18. Kokotovic, P. V., Kanellakopoulos, I., andKrstic, M.,On Letting Adaptive Control Be What It Is: Nonlinear Feedback, IFAC Symposia Series, Adaptive Systems in Control and Signal Processing, Pergamon Press, Tarrytown, New York, Vol. 8, pp. 79–85, 1993.

    Google Scholar 

  19. Freeman, R. A., andKokotovic, P. V.,Design of Soft Robust Nonlinear Control Laws, Automatica, Vol. 29, pp. 1425–1437, 1993.

    Article  Google Scholar 

  20. Kanellakopoulos, I., Krstic, M., andKokotovic, P. V.,κ-Adaptive Control of Output-Feedback Nonlinear Systems, Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, pp. 1061–1066, 1993.

  21. Qu, Z.,Robust Control of Nonlinear Uncertain Systems under Generalized Matching Conditions, Automatica, Vol. 29, pp. 985–998, 1993.

    Article  Google Scholar 

  22. Lee, C. S., andLeitmann, G.,A Drug Administration Problem, Mathematical and Computer Modelling, Vol. 15, pp. 79–90, 1991.

    Article  Google Scholar 

  23. Chen, Y. H., andLee, C. S.,Robust Control Design for a Two-Compartment Drug Administration Model, Dynamics and Control, Vol. 2, pp. 131–145, 1992.

    Article  Google Scholar 

  24. Lee, C. S., andLeitmann, G.,On Optimal Long-Term Management of Some Ecological Systems Subject to Uncertain Disturbances, International Journal of Systems Science, Vol. 14, pp. 979–994, 1983.

    Google Scholar 

  25. Mario, R. W., andSpong, M. W.,Nonlinear Control Techniques for Flexible Joint Manipulators, Proceedings of the 1986 IEEE Conference on Robotics and Automation, San Francisco, California, pp. 1026–1030, 1986.

  26. Leitmann, G., Lee, C. S., andChen, Y. H.,Decentralized Control of an Uncertain Multi-Reach River System, Optimal Control, Edited by R. Bulirsch, A. Miele, J. Stoer, and K. H. Well, Springer Verlag, Berlin, Germany, 1987.

    Google Scholar 

  27. Kelly, J. M., Leitmann, G., andSoldatos, A. G.,Robust Control of Base-Isolated Structures under Earthquake Excitation, Journal of Optimization Theory and Applications, Vol. 53, pp. 159–180, 1987.

    Article  Google Scholar 

  28. Chen, Y. H.,Adaptive Robust Control System Design: Using Information Related to the Bound of Uncertainty, Control Theory and Advanced Technology, Vol. 7, pp. 31–53, 1991.

    Google Scholar 

  29. Thorpe, J. S., andBarmish, B. R.,On Guaranteed Stability of Uncertain Linear Systems via Linear Control, Journal of Optimization Theory and Applications, Vol. 35, pp. 559–579, 1981.

    Article  Google Scholar 

  30. Krstic, M., andKokotovis, P. V.,Adaptive Nonlinear Control with Nonlinear Swapping, Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, pp. 1073–1080, 1993.

  31. Han, M. C., andChen, Y. H.,Robust Control Design for Flexible-Joint Manipulators: A Singular Perturbation Approach, Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, pp. 611–616, 1993.

  32. Chen, J. S., andChen, Y. H.,Robust Control of Nonlinear Uncertain Systems: A Feedback Linearization Approach, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, pp. 2515–2520, 1991.

  33. Hale, J. K.,Ordinary Differential Equations, Wiley-Interscience, New York, New York, 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia

    Y. H. Chen (Associate Professor)

Authors
  1. Y. H. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by C. T. Leondes

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y.H. Robust control design for a class of mismatched uncertain nonlinear systems. J Optim Theory Appl 90, 605–626 (1996). https://doi.org/10.1007/BF02189798

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02189798

Key Words

Search

Navigation