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An optimal control perspective on classical and quantum physical systems
Ortiz-Herrera, Roberto
Facultad de Ciencias Económicas y Administrativas 
Contreras-González, Mauricio
Villena, Marcelo
10.3390/sym15112033
Symmetry
2023
This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an openor closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.
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Control theory
Open- and closed-loop strategies
Pontryagin’s equations
Hamilton–Jacobi Equation
Canonical transformations
Quantum mechanics
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