It is well known that closing the loop around an exponentially stable, finite-dimensional, Linear, time-invariant plant with square transfer-function matrix G(s) compensated by a controller of the form (k/s)Gamma(0), where k is an element of R and Gamma(0) is an element of R(mxm), will result in an exponentially stable closed-loop system which achieves tracking of arbitrary constant reference signals, provided that (i) all the eigenvalues of G(0)Gamma(0) have positive real parts and (ii) the gain parameter k is positive and sufficiently small. In this paper we consider a rather general class of infinite-dimensional linear systems, called regular systems, for which convenient representations are known to exist, both in time and in frequency domain. The purpose of the paper is twofold : (i) we extend the above result to the class of exponentially stable regular systems and (ii) we show how the parameters k and Gamma(0) can be tuned adaptively. The resulting adaptive tracking controllers are not based on system identification or parameter estimation algorithms, nor is the injection of probing signals required.