2026/07/27 by A. J. Lazarus, Arnaud Lazarus, Emmanuel Trélat
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · doi:10.1137/25m1779000
openalex publication_date 2026/07/27 · openalex created_date 2026/07/28 · openalex updated_date 2026/07/28
Abstract. In this paper we study and solve a periodic optimal control problem for a bilinear harmonic oscillator (equivalently, for the Hill-type equation [Formula: see text] with bounded, sign-indefinite stiffness) 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 Schrödinger operators with a finite potential well, and the optimal dynamical Kapitza stabilization problem. We also briefly discuss the Floquet stability properties associated with the optimal periodic bang-bang control.