2020/06/11 by G., Mauricio Contreras, Villena, Marcelo
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2006.06162
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or 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 it can be described by a closed-loop feedback problem. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be thought of as constraints in a non-commutative space, then the momentum must be dependent on the position for any generic wave function. This implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. For the sake of exposition, we give a short review of control theory, and some familiar examples at the classical and quantum levels are analyzed.