Invariant manifolds and asymptotic properties of adaptive nonlinear stabilizers

IEEE Transactions on Automatic Control

Volumn 41, Issue 6, 1996, Pages 817-829

  Krstić, Miroslav ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SYSTEMS; CLOSED LOOP CONTROL SYSTEMS; CONVERGENCE OF NUMERICAL METHODS; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; SYSTEM STABILITY; VECTORS;

ADAPTIVE NONLINEAR STABILIZERS; CLOSED LOOP SYSTEM; LINEAR SYSTEMS; PERSISTENT EXCITATION;

ADAPTIVE CONTROL SYSTEMS;

EID: 0030164576     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.506234     Document Type: Article

References (16)

1. D. K. Arrowsmith and C. M. Place, An Introduction to Dynamical Systems. Cambridge, MA: Cambridge Univ. Press, 1990.
2. J. Carr, Applications of Centre Manifold Theory. New York: Springer-Verlag, 1981.
3. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983.
4. Z. P. Jiang and L. Praly, "Iterative designs of adaptive controllers for systems with nonlinear integrators," in Proc. 30th IEEE Conf. Decision Contr., Brighton, UK, Dec. 1991, pp. 2482-2487.
5. I. Kanellakopoulos, P. V. Kokotovieć, and A. S. Morse, "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1241-1253, 1991.
6. A. Kelley, "The stable, center-stable, center, center-unstable, and unstable manifolds," an appendix to Transversal Mappings and Flows by R. Abraham and J. Robhin. New York: Benjamin, 1967.
7. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
8. U. Kirchgraber and K. J. Palmer, Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearization. Longman, 1990.
9. M. Krstić, I. Kanellakopoulos, and P. V. Kokotovic, "Adaptive nonlinear control without overparametrization," Syst. Contr. Lett., vol. 19, pp. 177-185, 1992.
10. _, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
11. M. Krstić, R. Sepulchre, and L. Praly, "On the measure of global invariant manifolds of fixed points," Center for Control Engineering and Computation, Univ. California, Santa Barbara, Tech. Rep. CCEC 95-0228, 1995.
12. J. M. Ortega, Matrix Theory. New York: Plenum, 1987.
13. L. Praly, "Adaptive regulation: Lyapunov design with a growth condition," Int. J. Adaptive Contr. Signal Processing, vol. 6, pp. 329-351, 1992.
14. K. A. Ross, Elementary Analysis: The Theory of Calculus. New York: Springer-Verlag, 1980.
15. D. Taylor, P. V. Kokotović, R. Marino, and I. Kanellakopoulos, "Adaptive regulation of nonlinear systems with unmodeled dynamics," IEEE Trans. Automat. Contr., vol. 34, pp. 405-412, 1989.
16. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer-Verlag. 1990.