We present a control approach for autonomous vehicles based on deep reinforcement learning. A neural network agent is trained to map its estimated state to acceleration and steering commands given the objective of reaching a specific target state while considering detected obstacles. Learning is performed using state-of-the-art proximal policy optimization in combination with a simulated environment. Training from scratch takes five to nine hours. The resulting agent is evaluated within simulation and subsequently applied to control a full-size research vehicle. For this, the autonomous exploration of a parking lot is considered, including turning maneuvers and obstacle avoidance. Altogether, this work is among the first examples to successfully apply deep reinforcement learning to a real vehicle.