Symplectic Geometry in Optimal Control

Optimal control theory deals with finding input parameters to a dynamical system such that some objective is optimized, e.g., what is the best flight path to minimize fuel consumption? A central result in this field is the celebrated maximum principle developed by Lev Pontryagin and his students in the 1950s which recasts the optimal control problem as a boundary value problem of an associated Hamiltonian system. The field of symplectic geometry was developed to help understand Hamiltonian systems arising from classical mechanics. In this talk, I will present on some ways that symplectic geometry can be utilized for optimal control problems, e.g., energy and volume conservation.

William Clark received his BS degree in mechanical engineering from Ohio University in 2015 and his PhD in applied and interdisciplinary mathematics from the University of Michigan in 2020. Between 2020 and 2023, he was a Post-doctorate Research Fellow in the Department of Mathematics at Cornell University. He is currently an Assistant Professor in the Department of Mathematics at Ohio University. His research interests include geometric mechanics, control of nonlinear systems, analysis of discontinuous systems, and geometric structures in learning.