The Dirac--Bergmann approach to optimal control theory

• URL: http://arxiv.org/abs/2506.17610v1
• Date: Sat, 21 Jun 2025 06:23:22 GMT
• Title: The Dirac--Bergmann approach to optimal control theory
• Authors: Davit Aghamalyan, Aleek Maity, Varun Narasimhachar, V V Sreedhar,
• Abstract summary: We present a novel framework for optimal control in both classical and quantum systems.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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