Most differential drive platforms are equipped with two independent actuators and casters. The positions of the gravity center and the rotation center often do not coincide. This position difference, combined with the effect of unbalanced actuator dynamics on the motion, makes it difficult to properly control the platform. We propose an adaptive nonlinear controller system based on the Lyapunov stability theory that greatly improves the trajectory tracking performance of such platforms. The asymptotically stable kinematic controller takes into account the position difference and the effect of the unbalanced actuator dynamics. The dynamic controller has the desirable property that it requires minimal knowledge of the platform physical parameters. Validation was performed through simulation and several experiments conducted on a rear driven powered wheelchair. Comparative experimental studies suggested that the proposed adaptive control system performs better than a similar method presented in the literature for linear as well as curvilinear trajectory tracking. Furthermore, the control system exhibits good tracking performance on inclined plans and non smooth surfaces.