An Iterative Path Integral Stochastic Optimal Control Approach for Learning Robotic Tasks

2011 ◽  
Vol 44 (1) ◽  
pp. 11594-11601 ◽  
Author(s):  
Evangelos Theodorou ◽  
Freek Stulp ◽  
Jonas Buchli ◽  
Stefan Schaal
Keyword(s):  
Optimal Control ◽  
Path Integral ◽  
Stochastic Optimal Control ◽  
Control Approach ◽  
Robotic Tasks ◽  
Optimal Control Approach

scholarly journals The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1533 ◽  
Author(s):  
Jussi Lindgren ◽  
Jukka Liukkonen
Keyword(s):  
Optimal Control ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stochastic Optimal Control ◽  
Stochastic Approach ◽  
Heisenberg Uncertainty Principle ◽  
Control Approach ◽  
Heisenberg Uncertainty ◽  
Original Interpretation ◽  
Optimal Control Approach

We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the “thermodynamic equilibrium”. A stochastic process with a gradient structure is key in terms of understanding the uncertainty principle and such a framework comes naturally from the stochastic optimal control approach to quantum mechanics. The symmetry of the system is manifested in certain non-vanishing and invariant covariances between the four-position and the four-momentum. In terms of interpretation, the results allow one to understand the uncertainty principle through the lens of scientific realism, in accordance with empirical evidence, contesting the original interpretation given by Heisenberg.

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