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This paper presents a minimum-time feedback controller for maneuvering a non-holonomic vehicle. A trajectory planning algorithm that generates minimum-time trajectories for moving a vehicle from an arbitrary starting location to the origin is presented. Trajectories generated are used to train a neural network that computes instantaneous velocity and steering commands as a function of the current vehicle state. The proposed strategy is illustrated by developing a neural network based controller for backing up a truck. Computer simulations are presented that demonstrates the effectiveness of the proposed technique in the presence of disturbances.