In this paper, we propose a command governor-based adaptive control architecture for stabilizing uncertain dynamical systems with not only matched but also unmatched uncertainties and achieving the desired command following performance of a user-defined subset of the accessible states. In our proposed solution, online least-squares solutions for the matched and unmatched parameters are obtained through integration method and they are employed in the adaptive control framework. Specifically, the matched uncertainty is identified and its effect upon the system behavior is entirely attenuated. Moreover, using the unmatched uncertainty approximation obtained through radial basis function neural networks, the command governor signal is designed to achieve the desired command following performance of the user-defined subset of the accessible states. With this command governor-based model reference adaptive control architecture, the tracking error of the selected states can be made arbitrarily small by judiciously tuning the design parameters. In addition to the analysis of the closed-loop system stability using methods from the Lyapunov theory, our findings are also illustrated through numerical examples.