Analytical details are developed for a robust adaptive control strategy that combines switching control and on-line adaptive learning, for a class of nonlinear systems. The condition for stable learning is derived, guidelines for design parameter selection are provided, and the tradeoff between performance and chattering control effort is examined. The results of the study are summarized in the form of a constructive procedure for controller design for the class of systems.

Issue Section:
Technical Papers
Keywords:
nonlinear systems, robust control, adaptive control, learning systems, parameter estimation, control system synthesis
Topics:
Adaptive control, Design, Dynamics (Mechanics), Errors, Nonlinear systems, Tradeoffs, Uncertainty, Boundary layers, Control equipment, Robust control
1.
Slotine, J. E., and Li, W., 1991, Applied Nonlinear Control, Prentice Hall, NJ.
2.
Ioannou, P. A., and Sun, J., 1996, Robust Adaptive Control, Prentice Hall, NJ.
3.
Reed
,
J. S.
, and
Ioannou
,
P. A.
,
1989
, “
Instability Analysis and Robust Adaptive Control of Robotic Manipulators
,”
IEEE Trans. Rob. Autom.
,
5
(
3
), pp.
381
–
386
.
4.
Tsypkin, Y. Z., 1996, “Learning in Robust Control Systems,” Intelligent Control Systems: Theory and Applications, edited by Gupta, M. M., and Sinha, N. K., IEEE Press, pp. 86–100.
5.
Yao
,
B.
, and
Tomizuka
,
M.
,
1996
, “
Smooth Robust Adaptive Sliding Mode Control of Manipulators With Guaranteed Transient Performance
,”
ASME J. Dyn. Syst., Meas., Control
,
118
, pp.
764
–
765
.
6.
Slotine
,
J. E.
, and
Coetsee
,
J. A.
,
1986
, “
Adaptive Sliding Controller Synthesis for Nonlinear Systems
,”
Int. J. Control
,
43
(
6
), pp.
1631
–
1651
.
7.
Mistry
,
S. I.
,
Chang
,
S.
, and
Nair
,
S. S.
,
1996
, “
Indirect Control of a Class of Nonlinear Dynamic Systems
,”
IEEE Trans. Neural Netw.
,
7
, pp.
1015
–
1025
.
8.
Du
,
H.
, and
Nair
,
S. S.
,
1998
, “
Learning Control Design for a Class of Nonlinear Systems
,”
Eng. Applic. Artif. Intell.
,
11
, pp.
495
–
505
.
9.
Du, H., and Nair, S. S., 1997, “Robust Adaptive Compensation for a Class of Nonlinear Systems,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, DSC-61, pp. 579–586.
10.
Du
,
H.
, and
Nair
,
S. S.
,
2002
, “
Robust Adaptive Compensation for a Class of Nonlinear Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
124
(
1
), pp.
231
–
234
.
11.
Narendra, K. S., and Annaswamy, A., 1989, Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs.
12.
Sanner
,
R. M.
, and
Slotine
,
J.-J. E.
,
1992
, “
Gaussian Networks for Direct Adaptive Control
,”
IEEE Trans. Neural Netw.
,
3
(
6
), pp.
837
–
863
.
13.
Zhang
,
X.
,
Nair
,
S. S.
, and
Manring
,
N. D.
,
2002
, “
Robust Nonlinear Control of a Novel Indexing Valve Plate Pump-Simulation Studies
,”
ASME J. Dyn. Syst. Meas., Control
,
124
(
4
), pp.
613
–
616
.
Copyright © 2003
 by ASME
You do not currently have access to this content.