## Control Theory, Especially Distributed and Decentralized Control

*03 Mar 2004 16:13*

Yet another inadequate placeholder.

See also: Cybernetics; Filtering, State Estimation and Signal Processing; Multi-agent Systems; Neural Control of Action; Signal Transduction, Gene Expression and Control of Metabolism; Time Series Transducers

- Recommended:
- H. J. Kappen, "A linear theory for control of non-linear stochastic
systems", physics/0411119
= Physical
Review Letters
**95**(2005): 200201 ["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."] - Rudolf Kulhavy, Recursive Nonlinear Estimation: A Geometric Approach [Includes, explicitly, estimation in systems subject to external control]
- Maxim Raginsky, "Divergence-based characterization of fundamental limitations of adaptive dynamical systems", arxiv:1010.2286
- Stengel, Optimal Control and Estimation
- Mathukumalli Vidyasagar, A Theory of Learning and Generalization: With Applications to Neural Networks and Control Systems [Control problems only arise in the last chapter, but the previous chapters really are needed to build up to that one. Mini-review]
- Norbert Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine

- To read:
- Karl Astrom, Pedro Albertos, Mogens Blanke, Alberto Isidori, Walter Schaufelberger and Ricardo Sanz (eds.), Control of Complex Systems
- John Bechhoefer, "Feedback for physicists: A tutorial essay on
control", Review of
Modern Physics
**77**(2005): 783 - A. Bensoussan, Stochastic Control of Partially Observable Systems
- Byron Boots, Sajid M. Siddiqi, Geoffrey J. Gordon, "Closing the Learning-Planning Loop with Predictive State Representations", arxiv:0912.2385
- Ruslan K. Chornei, Hans Daduna and Pavel S. Knopov, Control of Spatially Structured Random Processes and Random Fields with Applications [Blurb]
- J. H. Davis, Foundations of Deterministic and Stochastic Control
- Pablo A. Iglesias and Brian P. Ingalls (eds.), Control Theory and Systems Biology [blurb]
- Brian P. Ingalls, Eduardo D. Sontag and Yuan Wang, "Measurement to Error Stability: a Notion of Partial Detectability for Nonlinear Systems," math.OC/0202098
- H. J. Kappen, "Path integrals and symmetry breaking for optimal control theory", Journal of Statistical Mechanics: Theory and Experiment (2005): P11011, physics/0505066
- Mikhail Krichman, Eduardo D. Sontag and Yuan Wang, "Input-Output-to-State Stability," math.OC/9911233
- Harold J. Kushner and Paul G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time
- Winfried Lohmiller and Jean-Jacques E. Slotine, "Contraction Analysis of Nonlinear Distributed Systems", math-ph/0403027
- D. McFadden, "On the Controllability of Decentralized Microeconomic Systems," in H. W. Kuhn and G. P. Szego (eds.), Mathematical Systems Theory and Economics (Springer-Verlag, 1967), pp. 221--239
- Andrew Newman, Modeling and Reduction [Ph.D. thesis, UMCP, 1999]
- Gilles Pages, Huyen Pham and Jacques Printems, "An Optimal
Markovian Quantization Algorithm for Multi-Dimensional Stochastic Control
Problems", Stochastics and
Dynamics
**4**(2004): 501--545 [From the abstract: "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."] - Huyen Pham, "On some recent aspects of stochastic control and their applications", math.PR/0509711 [Review paper. Looks quite nice.]
- Dawn T. Robinson, "Control Theories in Sociology",
Annual
Review of Sociology
**33**(2007): 157--174 - Dragoslav D. Siljak, Decentralized Control of Complex Systems
- Jan C. Willems, Analysis of Feedback Systems