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The quantum dark side of the optimal control theory

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  • G., Mauricio Contreras
  • Peña, Juan Pablo

Abstract

In a recent article, a generic optimal control problem was studied from a physicist’s point of view (Contreras et al. 2017). Through this optic, the Pontryagin equations are equivalent to the Hamilton equations of a classical constrained system. By quantizing this constrained system, using the right ordering of the operators, the corresponding quantum dynamics given by the Schrödinger equation is equivalent to that given by the Hamilton–Jacobi–Bellman equation of Bellman’s theory. The conclusion drawn there were based on certain analogies between the equations of motion of both theories.

Suggested Citation

  • G., Mauricio Contreras & Peña, Juan Pablo, 2019. "The quantum dark side of the optimal control theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 450-473.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:450-473
    DOI: 10.1016/j.physa.2018.09.134
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    References listed on IDEAS

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    Cited by:

    1. Mauricio Contreras G, 2020. "An Application of Dirac's Interaction Picture to Option Pricing," Papers 2010.06747, arXiv.org.

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