Optimal control theory with arbitrary superpositions of waveforms

Selina Meister, Jürgen T. Stockburger, Rebecca Schmidt, Joachim Ankerhold

Published 2014-08-27Version 1

Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms. Since this type of constraint is not time-local, Optimal Control Theory cannot be used without modifications. Simplex methods, used as a substitute in this case, tend to be less efficient and less reliable than Optimal Control Theory. In this paper, we present an extension to Optimal Control Theory which allows gradient-based optimization for superpositions of arbitrary waveforms. Its key is the use of the Moore-Penrose pseudoinverse as an efficient means of transforming from a time-local to a waveform-based description. To illustrate this optimization technique, we study the parametrically driven harmonic oscillator as model system and reduce its energy, considering both Hamiltonian dynamics and open-system dynamics. We demonstrate the viability and efficiency of the method for these test cases.