Deterministic adaptive control with slowly varying parameters: An averaging analysis

International Journal of Control

Volumn 64, Issue 1, 1996, Pages 99-125

  Solo, Victor ^a,b  

^a Johns Hopkins University   (United States)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; CONTROL EQUIPMENT; CONTROL SYSTEM ANALYSIS; PARAMETER ESTIMATION; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

AVERAGING ANALYSIS; DETERMINISTIC ADAPTIVE CONTROL; SLOWLY VARYING PARAMETERS;

ADAPTIVE CONTROL SYSTEMS;

EID: 0030146829     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207179608921619     Document Type: Article

References (16)

1. Anderson, B. D. O., and Johnstone, R. M., 1983, Adaptive systems and time varying plants. International Journal of Control, 37, 367-377.
2. Balachandra, M., and Sethna, P. R., 1975, A generalization of the method of averaging for systems with two time scales, Archives of Rational Mechanical Analysis, 58.
3. Bodson, M., Sastry, S., Anderson, B. D. O., Mareels, I., and Bitmead, R. R., 1986, Nonlinear averaging theorems and the determination of parameter convergence rates in adaptive control. Systems Control Letters, 7, 145-157.
4. Bogoliubov, N. N., and Mitropolsky, Y., 1961, Asymptotic Methods in Nonlinear Mechanics (New York: Gordon and Breach).
5. Coppel, W. A., 1978, Dichotomies in Stability Theory. Lecture Notes in Mathematics, No. 629 (Berlin, New York: Springer-Verlag).
6. Fu, L. C., Bodson, M., and Sastry, S., 1987, New stability theorems for averaging and their application to the convergence analysis of adaptive identification and control schemes. Singular Perturbations and Asymptotic Analysis in Control Systems, edited by P. Kokotovic, A. Bensoussan and G. Blankenship, Lecture notes in Control and Information Sciences, Vol. 90 (Springer-Verlag).
7. Freidlin, M. I., and Wentzell, A. D., 1984, Random Perturbations of Dynamical Systems (New York: Springer-Verlag).
8. Gikhman, I. I., 1952, Poporodu Odnoi Teoremy. Bogolybova. Ukrain. Mat. Zh., 4, 215-218.
9. Kreisselmeier, G., 1986, Adaptive control of a class of slowly time varying plants. Systems Control Letters, 8, 97-103.
10. KuShner, H., 1984, Approximation and Weak Convergence Methods for Random Process (Cambridge, Massachusetts, U.S.A.: MIT Press).
11. Middleton, R. H., and Goodwin, G. C, 1988, Adaptive control of time-varying linear systems, IEEE Transactions on Automatic Control, 33, 150-155.
12. Narendra, K., and Valavani, L., 1979, Stable adaptive controller design-direct control. IEEE Transactions on Automatic Control, 32, 570-583.
13. Riedle, B. D., and Kokotovic, P. V., 1986, Integral manifolds of slow adaptation. IEEE Transactions on Automatic Control, 31, 316-324.
14. Tsakalis, K. S., and Ioannou, P. A., 1989, Adaptive control of linear time varying plants: a new model reference controller structure. IEEE Transactions on Automatic Control, 34, 1038-1046.
15. Solo, V., 1991, Averaging methods for adaptive systems with time varying parameters: infinite time results, in preparation.
16. Vidyasagar, M., 1978, Nonlinear Systems Analysis (New York: Prentice Hall).