The quantum dark side of the optimal control theory

Mauricio Contreras G. and Juan Pablo Peña

Physica A: Statistical Mechanics and its Applications, 2019, vol. 515, issue C, 450-473

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.

Keywords: Optimal control theory; Pontryagin’s equations; Hamilton–Jacobi–Bellman equation; Constrained systems; Dirac’s method; Quantum mechanics (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:515:y:2019:i:c:p:450-473

DOI: 10.1016/j.physa.2018.09.134

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