This paper presents two adaptive control laws that have improved parameter conver-gence properties. These adaptive control laws are derived through the framework of Model Reference Adaptive Control and are applicable to plants with structured or unstructured modeling uncertainty. The presented adaptive control laws use both recorded and current data concurrently to improve parameter convergence and are shown to have a stability proof. The first method, termed as concurrent learning adaptive control, increases the rank of standard gradient descent based adaptive laws and guarantees that the adaptive weights approach the ideal weights if the recorded data meets a verifiable condition on linear independence. The second method introduces a least squares based modification term that drives the adaptive weights to an estimate of the ideal weights computed online using recorded data. This modification term guarantees the asymptotic stability of the tracking error and convergence of adaptive weights if a condition on linear independence of the recorded data is met. Expected improvement in parameter convergence and tracking error is demonstrated through adaptive autopilot design for a fixed wing unmanned aircraft and through simulation studies of control of wing rock dynamics.