A meaningful optimal control problem in quantum and classical physics

TL;DR

This paper addresses a complex optimal control problem motivated by quantum and classical physics, employing advanced control theory methods to connect it with physical problems like Schrödinger ground states and Kapitza stabilization.

Contribution

It introduces a novel optimal control problem and demonstrates its solutions and relationships to key physics problems, advancing the application of control theory in physics.

Findings

Solution methods for the control problem are developed.

Connections to Schrödinger ground state computation are established.

Links to Kapitza stabilization are demonstrated.

Abstract

In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is not easy to solve and we resort to various elaborated methods of optimal control theory. We finally show its relationships to two problems in physics: the computation of the ground state for 1D Schr{\"o}dinger operators with a finite potential well, and the optimal dynamical Kapitza stabilization problem.