DE Seminar: William Clark

Title: Symplectic Geometry in Optimal Control and Impulsive Systems

Speaker: William Clark

Abstract: 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.

In this talk, I will present the version of the maximum principle for discontinuous control systems which results in the study of impulsive Hamiltonian systems. The canonical symplectic structure remains invariant under the impulses which allows for some tools from symplectic geometry to be utilized. This talk will conclude with a discussion on where this theory is inadequate.