Contact Geometry of the Pontryagin Maximum Principle

This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle—such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers—have natural contact-geometric interpretations. We then exploit the contact-geometric formulation to give a simple derivation of the transversality condition for optimal control with terminal cost.