While adaptive control theory has been used in numerous applications to achieve given system stabilisation or command following criteria without excessive reliance on mathematical models, the ability to obtain a predictable transient performance is still an important problem - especially for applications to safety-critical systems and when there is no a-priori knowledge on upper bounds of existing system uncertainties. To address this problem, we present a new approach to improve the transient performance of adaptive control architectures. In particular, our approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimisation procedure to minimise the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. We provide a detailed stability analysis of the proposed approach, discuss the practical aspects of its implementation, and illustrate its efficacy on a numerical example.