ADAPTIVE LAMBDA-TRACKING FOR A CLASS OF INFINITE-DIMENSIONAL SYSTEMS

For a class of high-gain stabilizable multivariable linear infinite-di mensional systems we present an adaptive control law which achieves ap proximate asymptotic tracking in the sense that the tracking error ten ds asymptotically to a ball centred at 0 and of arbitrary prescribed r adius lambda>0. This control strategy, called lambda-tracking, combine s proportional error feedback with a simple nonlinear adaptation of th e feedback gain. It does not involve any parameter estimation algorith ms, nor is it based on the internal model principle. The class of refe rence signals is W-I,W-infinity, the Sobolev space of absolutely conti nuous functions which are bounded and have essentially bounded derivat ive. The control strategy is robust with respect to output measurement noise in W-I,W-infinity , and bounded input disturbances. We apply ou r results to retarded systems and integrodifferential systems. (C) 199 8 Elsevier Science B.V. All rights reserved.