Contact Geometry of the Pontryagin Maximum Principle

Abstract

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.

arXiv comment10 pages, 4 figures

References in corpus (1)

• Geometric Approach to Pontryagin's Maximum Principle

Cited by in corpus (4)

• Contact variational integrators
• Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
• A contact covariant approach to optimal control with applications to sub-Riemannian geometry
• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold