The Dirac--Bergmann approach to optimal control theory

Davit Aghamalyan, Aleek Maity, Varun Narasimhachar, V V Sreedhar

Published 2025-06-21Version 1

We present a novel framework for optimal control in both classical and quantum systems. Our approach leverages the Dirac--Bergmann algorithm: a systematic method for formulating and solving constrained dynamical systems. In contrast to the standard Pontryagin principle, which is used in control theory, our approach bypasses the need to perform a variation to obtain the optimal solution. Instead, the Dirac--Bergmann algorithm generates the optimal solution dynamically. The efficacy of our framework is demonstrated through two quintessential examples: the classical and quantum brachistochrone problems, the latter relevant for quantum technological applications.