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Entropy 2015, 17(5), 3352-3375; doi:10.3390/e17053352

Nonlinear Stochastic Control and Information Theoretic Dualities: Connections, Interdependencies and Thermodynamic Interpretations

1
The Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta,GA 30332-0150, USA
2
Institute of Robotics and intelligent Machines, Georgia Institute of Technology, Atlanta, GA30332-0150, USA 
Academic Editor: Kevin H. Knuth
Received: 2 February 2015 / Revised: 21 April 2015 / Accepted: 29 April 2015 / Published: 15 May 2015
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Abstract

In this paper, we present connections between recent developments on the linearly-solvable stochastic optimal control framework with early work in control theory based on the fundamental dualities between free energy and relative entropy. We extend these connections to nonlinear stochastic systems with non-affine controls by using the generalized version of the Feynman–Kac lemma. We present alternative formulations of the linearly-solvable stochastic optimal control framework and discuss information theoretic and thermodynamic interpretations. On the algorithmic side, we present iterative stochastic optimal control algorithms and applications to nonlinear stochastic systems. We conclude with an overview of the frameworks presented and discuss limitations, differences and future directions. View Full-Text
Keywords: Stochastic Optimal Control; Information Theory; Thermodynamics Stochastic Optimal Control; Information Theory; Thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Theodorou, E.A. Nonlinear Stochastic Control and Information Theoretic Dualities: Connections, Interdependencies and Thermodynamic Interpretations. Entropy 2015, 17, 3352-3375.

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