# Adaptive λ-[lambda]-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius lambda>0. This control strategy, called lambda-tracking, 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 internal model principle. The class of reference signals is W1,00, 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 W1,00 and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems.

### Cite

Citation style:
Ilchmann Prof. Dr., A., Logemann, H., 2005. Adaptive $\lambda$-[lambda]-tracking for a class of infinite-dimensional systems.