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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
Kullback-Leibler divergence between the probabilistic eﬀect of a
control p (xt +1 |xt , ut ) compared to uncontrolled dynamics
p (xt +1 |xt , ut = 0)  (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 Kullback-Leibler 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
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
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at al (eds), chap 12, 269, MIT Press 2006. Free online.  H.J. Kappen, Optimal conrol theory and the linear Bellman Equation. Book chapter. Free online.  H.J. Kappen, Path integrals and symmetry breaking for optimal control theory. Journal of statistical
mechanics: theory and Experiment, 11011, 2005.  E. Libby, T.J. Perkins, and P.S. Swain Noisy information processing through transcriptional regulation,
PNAS 104, 7151, 2007.  T.J Kobayashi and A. Kamimura,Dynamics of intracellular information decoding, Phys. Biol. 8, 055007,
2011.  K.J. ˚str¨m and R.J. Murray, Feedback systems, Princeton University Press. 2008. Free online.
Ao  J. Bechhoefer, Feedback for physicists: A tutorial essay on control, Reviews of Modern Physics, 77, 783,
2005. Free to you online.  R.S. Sutton and A.G. Barto, Reinforcement learning, MIT Press, 1998. Free online.  J. Zabczyk, Classical control theory, 2001. Lecture notes online.  J. Zabczyk, Mathematical control theory, Birkauser, 1995. Free to IC students.  E. Sontag, Mathematical control theory, Springer, 1998. Free online.  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