For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an aclaptive control law which achieves approximatc asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius,1 >0. This control strategy, called,t{racking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the intemal model principle. The class of reference signals is l,ltt,n, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in Wt'* and bounded input disturbances. We apply our results to retarded systcms and integrodifferential systems. @ 1998 Elsevier Science B.V. All rights reserved. Keyt"ords; Adaptive control; Tracking; High-gain control; Infinite-dimensional systems; Functional differential equationsl Integrodifferential equations
[1]
Frank Allgöwer,et al.
High-gain adaptive λ-tracking for nonlinear systems
,
1997,
Autom..
[2]
Hartmut Logemann,et al.
Input‐output theory of high‐gain adaptive stabilization of infinite‐dimensional systems with non‐linearities
,
1988
.
[3]
M. Vidyasagar.
A note on time invariance and causality
,
1983
.
[4]
Achim Ilchmann,et al.
Adaptive Multivariable pH Regulation of a Biogas Tower Reactor
,
1998,
Eur. J. Control.
[5]
Diederich Hinrichsen,et al.
Destabilization by output feedback
,
1992,
Differential and Integral Equations.
[6]
Eugene P. Ryan,et al.
Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise
,
1994,
Autom..
[7]
Achim Ilchmann,et al.
Non-Identifier-Based High-Gain Adaptive Control
,
1993
.