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    <title>Notebooks   </title>
    <link>http://bactra.org/notebooks</link>
    <description>Cosma's Notebooks</description>
    <language>en</language>

  <item>
    <title>Control Theory, Especially Distributed and Decentralized Control</title>
    <link>http://bactra.org/notebooks/2004/03/03#control</link>
    <description>
&lt;P&gt;See also:
	&lt;a hrf=&quot;cybernetics.html&quot;&gt;Cybernetics&lt;/a&gt;;
	&lt;a href=&quot;filtering.html&quot;&gt;Filtering, State Estimation and Signal
Processing&lt;/a&gt;;
	&lt;a href=&quot;multi-agent-systems.html&quot;&gt;Multi-agent Systems&lt;/a&gt;;
	&lt;a href=&quot;seriatim.html&quot;&gt;Neural Control of Action&lt;/a&gt;;
	&lt;a href=&quot;signal-transduction.html&quot;&gt;Signal Transduction, Gene Expression
and Control of Metabolism&lt;/a&gt;;
	&lt;a href=&quot;time-series.html&quot;&gt;Time Series&lt;/a&gt;
	&lt;a href=&quot;transducers.html&quot;&gt;Transducers&lt;/a&gt;
	&lt;/ul&gt;

&lt;ul&gt;Recommended:
	&lt;li&gt;H. J. Kappen, &quot;A linear theory for control of non-linear stochastic
systems&quot;, &lt;a href=&quot;http://arxiv.org/abs/physics/0411119&quot;&gt;physics/0411119&lt;/a&gt;
= &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.95.200201&quot;&gt;&lt;cite&gt;Physical
Review Letters&lt;/cite&gt; &lt;strong&gt;95&lt;/strong&gt; (2005): 200201&lt;/a&gt; [&quot;We address the
role of noise and the issue of efficient computation in stochastic optimal
control problems. We consider a class of non-linear control problems that can
be formulated as a path integral and where the noise plays the role of
temperature. The path integral displays symmetry breaking and there exist a
critical noise value that separates regimes where optimal control yields
qualitatively different solutions. The path integral can be computed
efficiently by Monte Carlo integration or by Laplace approximation, and can
therefore be used to solve high dimensional stochastic control problems.&quot;]
	&lt;li&gt;Rudolf Kulhavy, &lt;cite&gt;Recursive Nonlinear Estimation: A Geometric
Approach&lt;/cite&gt; [Includes, explicitly, estimation in systems subject to
external control]
	&lt;li&gt;Stengel, &lt;cite&gt;Optimal Control and Estimation&lt;/cite&gt;
	&lt;li&gt;Mathukumalli Vidyasagar, &lt;cite&gt;A Theory of Learning and
Generalization: With Applications to Neural Networks and Control Systems&lt;/cite&gt;
[Control problems only arise in the last chapter, but the previous chapters
really are needed to build up to that
one.  &lt;a href=&quot;../weblog/algae-209-01.html#vidyasagar&quot;&gt;Mini-review&lt;/a&gt;]
	&lt;li&gt;&lt;a href=&quot;wiener.html&quot;&gt;Norbert Wiener&lt;/a&gt;, &lt;cite&gt;Cybernetics: Or
Control and Communication in the Animal and the Machine&lt;/a&gt;
	&lt;/ul&gt;

&lt;ul&gt;To read:
	&lt;li&gt;Karl Astrom, Pedro Albertos, Mogens Blanke, Alberto Isidori, Walter
Schaufelberger and Ricardo Sanz (eds.), &lt;cite&gt;Control of Complex
Systems&lt;/cite&gt;
	&lt;li&gt;John Bechhoefer, &quot;Feedback for physicists: A tutorial essay on
control&quot;, &lt;a href=&quot;http://dx.doi.org/10.1103/RevModPhys.77.783&quot;&gt;&lt;cite&gt;Review of
Modern Physics&lt;/cite&gt; &lt;strong&gt;77&lt;/strong&gt; (2005): 783&lt;/a&gt;
	&lt;li&gt;A. Bensoussan, &lt;cite&gt;Stochastic Control of Partially Observable
Systems&lt;/cite&gt;
	&lt;li&gt;Ruslan K. Chornei, Hans Daduna and Pavel S. Knopov, &lt;cite&gt;Control
of Spatially Structured Random Processes and Random Fields with
Applications&lt;/cite&gt;
[&lt;a
href=&quot;http://www.springer.com/sgw/cda/frontpage/0,11855,4-0-22-107907394-0,00.html&quot;&gt;Blurb&lt;/a&gt;]
	&lt;li&gt;J. H. Davis, &lt;cite&gt;Foundations of Deterministic and Stochastic
Control&lt;/cite&gt;
	&lt;li&gt;Randa Herzallah and David Lowe, &quot;Robust Control of Nonlinear
Stochastic Systems by Modelling Conditional Distributions of Control Signals&quot;
[&lt;a
href=&quot;http://www.ncrg.aston.ac.uk/cgi-bin/tr_avail.pl?trnumber=NCRG/2003/009&quot;&gt;Link
to downloads&lt;/a&gt;]
	&lt;li&gt;Pablo A. Iglesias and Brian P. Ingalls (eds.), &lt;cite&gt;Control Theory and Systems Biology&lt;/cite&gt; [&lt;a href=&quot;http://mitpress.mit.edu/978-0-262-01334-5&quot;&gt;blurb&lt;/a&gt;]
	&lt;li&gt;Brian P. Ingalls, Eduardo D. Sontag and Yuan Wang, &quot;Measurement to
Error Stability: a Notion of Partial Detectability for Nonlinear Systems,&quot; &lt;a
href=&quot;http://arxiv.org/abs/math.OC/0202098&quot;&gt;math.OC/0202098&lt;/a&gt;
	&lt;li&gt;H. J. Kappen, &quot;Path integrals and symmetry breaking for optimal
control theory&quot;, &lt;a
href=&quot;http://arxiv.org/abs/physics/0505066&quot;&gt;physics/0505066&lt;/a&gt;
	&lt;li&gt;Mikhail Krichman, Eduardo D. Sontag and Yuan Wang,
&quot;Input-Output-to-State Stability,&quot; &lt;a
href=&quot;http://arxiv.org/abs/math.OC/9911233&quot;&gt;math.OC/9911233&lt;/a&gt;
	&lt;li&gt;Harold J. Kushner and Paul G. Dupuis, &lt;cite&gt;Numerical Methods for
Stochastic Control Problems in Continuous Time&lt;/cite&gt;
	&lt;li&gt;Winfried Lohmiller and Jean-Jacques E. Slotine, &quot;Contraction
Analysis of Nonlinear Distributed Systems&quot;,
&lt;a href=&quot;http://arxiv.org/abs/math-ph/0403027&quot;&gt;math-ph/0403027&lt;/a&gt;
	&lt;li&gt;D. McFadden, &quot;On the Controllability of Decentralized Microeconomic
Systems,&quot; in H. W. Kuhn and G. P. Szego (eds.), &lt;cite&gt;Mathematical Systems
Theory and Economics&lt;/cite&gt; (Springer-Verlag, 1967), pp. 221--239
	&lt;li&gt;&lt;a href=&quot;http://www.isr.umd.edu/~newman/&quot;&gt;Andrew
Newman&lt;/a&gt;, &lt;cite&gt;Modeling and Reduction&lt;/cite&gt; [Ph.D. thesis, UMCP,
1999]
	&lt;li&gt;Gilles Pages, Huyen Pham and Jacques Printems, &quot;An Optimal
Markovian Quantization Algorithm for Multi-Dimensional Stochastic Control
Problems&quot;, &lt;a
href=&quot;http://dx.doi.org/10.1142/S0219493704001231&quot;&gt;&lt;citE&gt;Stochastics and
Dynamics&lt;/cite&gt; &lt;strong&gt;4&lt;/strong&gt; (2004): 501--545&lt;/a&gt; [From the abstract: &quot;We
propose a probabilistic numerical method based on optimal quantization to solve
some multi-dimensional stochastic control problems.... [C]ontrolled diffusions
with most components control free.  The Euler scheme of the uncontrolled
diffusion part is approximated by a discrete time process obtained by a nearest
neighbor projection on some grids optimally fitted to its dynamics.  The result
process is also designed to preserve the Markov property with respect to the
filtration of the Euler scheme.&quot;]
	&lt;li&gt;Huyen PHam, &quot;On some recent aspects of stochastic control and their
applications&quot;, &lt;a
href=&quot;http://arxiv.org/abs/math.PR/0509711&quot;&gt;math.PR/0509711&lt;/a&gt; [Review paper.
Looks quite nice.]
	&lt;li&gt;Aude Rondepierre and Jean-Guillaume Dumas, &quot;Algorithms for Hybrid
Optimal Control&quot;, &lt;a
href=&quot;http://arxiv.org/abs/math.OC/0502172&quot;&gt;math.OC/0502172&lt;/a&gt; [&quot;We consider a
non linear ordinary differential equation and want to control its behavior so
that it reaches a target by minimizing a cost function. Our approach is to use
hybrid systems to solve this problem: the complex dynamic is replaced by
piecewise affine approximations which allow an analytical resolution. The
sequence of affine models then forms a sequence of states of a hybrid
automaton. Given an optimal sequence of states, we are then able to traverse
the automaton till the target, locally insuring the optimality.&quot;]
	&lt;li&gt;M. M. Seron, J. H. Braslavsky and G. C. Goodwin, &lt;cite&gt;Fundamental
Limitations in Filtering and Control&lt;/cite&gt; [&lt;a
href=&quot;http://murray.newcastle.edu.au/users/postgrads/brasky/book/download.html&quot;&gt;Website&lt;/a&gt;,
with full-text PDF and errata]
	&lt;li&gt;Dragoslav D. Siljak, &lt;cite&gt;Decentralized Control of Complex
Systems&lt;/cite&gt;
	&lt;/ul&gt;
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