Design and Comparison of Globally Stabilizing Controllers for an Uncertain Nonlinear System

  • R. A. Freeman
  • P. V. Kokotovic
Chapter
Part of the Progress in Systems and Control Theory book series (PSCT, volume 12)

Abstract

We review various integrator backstepping design procedures for generating globally stabilizing controllers for uncertain nonlinear systems. By way of a case study of a simple planar system, we demonstrate how these procedures can be combined to produce new classes of stabilizing controllers. We present eight different backstepping controllers for the planar system and compare their structural properties and simulated performance.

Keywords

Control Signal Lyapunov Function Uncertain Nonlinear System Adaptive Backstepping Global Boundedness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. R. Corless and G. Leitman, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Transactions on Automatic Control, vol. AC-26, no. 5, pp. 1139–1144, 1981.CrossRefGoogle Scholar
  2. [2]
    F. Esfandiari and H. K. Khalil, Stability analysis of a continuous implementation of variable structure control, IEEE Transactions on Auto-matic Control, vol. 36, no. 5, pp. 616–620, 1991.CrossRefGoogle Scholar
  3. [3]
    R. A. Freeman and P. V. Kokotovic, Backstepping design of robust controllers for a class of nonlinear systems. In preparation, 1991.Google Scholar
  4. [4]
    Z. P. Jiang and L. Praly, Iterative designs of adaptive controllers for systems with nonlinear integrators. Submitted for presentation at The 30th IEEE Conference on Decision and Control, 1991.Google Scholar
  5. [5]
    I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, Systematic design of adaptive controllers for feedback linearizable systems, IEEE Transactions on Automatic Control, vol. 36, no. 11, 1991.Google Scholar
  6. [6]
    I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, A toolkit for nonlinear feedback design, Tech. Rep. CCEC-91–0619, Center for Control Engineering and Computation, Electrical and Computer Engineering, University of California, Santa Barbara, 1991.Google Scholar
  7. [7]
    H. K. Khalil, Nonlinear Systems. New York: Macmillan Publishing Company, 1992.Google Scholar
  8. [8]
    L. Praly, July 1991. Personal communication.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • R. A. Freeman
    • 1
  • P. V. Kokotovic
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations