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Unformatted text preview: at this approach can be considered as a special case
of a more general approach to control that looks at the
KullbackLeibler divergence between the probabilistic eﬀect of a
control p (xt +1 xt , ut ) compared to uncontrolled dynamics
p (xt +1 xt , ut = 0) [12] (take a look it’s a great read). If the
distribution associated with my control is close to that of my
passive dynamics I consider this low cost. I thus pick up a term in
my cost function which is the KullbackLeibler divergence between
p (xt +1 xt , ut ) and p (xt +1 xt , ut = 0). There is an energetic
interpretation to this since the amount of work one can extract if
p (xt +1 xt , ut ) relaxes to p (xt +1 xt , ut = 0) is speciﬁed by the
KullbackLeibler divergence.
Nick Jones Elements of Stochastic Optimal Control: ICDNS Summarizing the week I’ll give a summary of the ideas that we’ve investigated this week. Nick Jones Elements of Stochastic Optimal Control: ICDNS Bibliography
[1] E. Todorov, Optimal control theory, In Bayesian Brain: Probabilistic Approaches to Neural Coding, Doya K
at al (eds), chap 12, 269, MIT Press 2006. Free online. [2] H.J. Kappen, Optimal conrol theory and the linear Bellman Equation. Book chapter. Free online. [3] H.J. Kappen, Path integrals and symmetry breaking for optimal control theory. Journal of statistical
mechanics: theory and Experiment, 11011, 2005. [4] E. Libby, T.J. Perkins, and P.S. Swain Noisy information processing through transcriptional regulation,
PNAS 104, 7151, 2007. [5] T.J Kobayashi and A. Kamimura,Dynamics of intracellular information decoding, Phys. Biol. 8, 055007,
2011. [6] K.J. ˚str¨m and R.J. Murray, Feedback systems, Princeton University Press. 2008. Free online.
Ao [7] J. Bechhoefer, Feedback for physicists: A tutorial essay on control, Reviews of Modern Physics, 77, 783,
2005. Free to you online. [8] R.S. Sutton and A.G. Barto, Reinforcement learning, MIT Press, 1998. Free online. [9] J. Zabczyk, Classical control theory, 2001. Lecture notes online. [10] J. Zabczyk, Mathematical control theory, Birkauser, 1995. Free to IC students. [11] E. Sontag, Mathematical control theory, Springer, 1998. Free online. [12] E. Todorov, Eﬃcient computation of optimal actions, PNAS, 11478, 83, 2009. Nick Jones Elements of Stochastic Optimal Control: ICDNS...
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This document was uploaded on 03/01/2014 for the course EE 208 at Imperial College.
 Spring '14
 NickJones
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