A novel control design is presented for the adaptive control of a general MIMO system with a gradient-based composite adaptive update law. The composite update law is driven by tracking and prediction errors with a fixed adaptation gain. An innovative scheme is developed in a swapping procedure that makes use of the recently developed Robust Integral of the Sign of the Error (RISE) technique to generate the prediction error even in the presence of nonlinear-in-the-parameter uncertainties. A Lyapunov-based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi-global asymptotic stability for the tracking errors.