## Control Theory, Especially Distributed and Decentralized Control

*03 Mar 2004 16:13*

Yet another inadequate placeholder.

If I were a better teacher, I'd have a way of making Hamilton-Jacobi-Bellman and the maximum principle intuitive to students, at least ones who've grasped Lagrange multipliers. I do not. (Pinch and Weitzman are both approaches to this, but neither will quite work for my students.)

- See also:
- Calculus of Variations and Optimal Control Theory
- Cybernetics
- Economics
- Filtering, State Estimation and Signal Processing
- Koopman Operators for Modeling Dynamical Systems and Time Series
- Multi-agent Systems
- Neural Control of Action
- Optimization
- Planned Economies
- Sequential Decision-Making Under Stochastic Uncertainty
- Signal Transduction, Gene Expression and Control of Metabolism
- Time Series
- Transducers

- Recommended, big picture (totally inadequate):
- Benjamin Recht, An Outsider's Tour of Reinforcement Learning [and control theory more broadly]
- Robert F. Stengel, Optimal Control and Estimation
- Norbert Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine

- Recommended, close-ups (if possible even more inadequate):
- Yu-Chi Ho, Marcia P. Kastner and Eugene Wong, "Teams, Signaling, and Information Theory", IEEE Transactions on Automatic Control
**23**(1978): 305--312 [Ungated copy via Prof. Wong. Thanks to Maxim Raginsky for the reference.] - 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
- 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]

- To read:
- Pedro Albertos and Iven Mareels, Feedback and Control for Everyone
- Anuradha M. Annaswamy, Alexander L. Fradkov, "A Historical Perspective of Adaptive Control and Learning", arxiv:2108.11336
- Ari Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh, Ergodic Control of Diffusion Processes
- Karl J. Astrom and P. R. Kumar, "Control: A Perspective", Automatica
**50**(2014): 3--43 [Thanks to Maxim Raginsky for the reference] - 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
- J. H. Davis, Foundations of Deterministic and Stochastic Control
- I. Gumowski and C. Mira, Optimization in Control Theory and Practice
- Joao P. Hespanha, Daniel Liberzon and A. Stephen Morse, "Hysteresis-based switching algorithms for supervisory control of uncertain systems",
Automatica
**39**(2003): 263--272 - Pablo A. Iglesias and Brian P. Ingalls (eds.), Control Theory and Systems Biology
- M. Ikeda, "Decentralized control of large scale systems", pp. 219--242 in H. Nijmeijer and J. M. Schumacher (eds.), Three Decades of Mathematical System Theory: A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems (1989)
- 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
- Christopher M. Kellett and Philipp Braun, Introduction to Nonlinear Control: Stability, Control Design, and Estimation [Not in JSTOR yet but the publisher's usually good about that...]
- 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
- 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 - Huyen Pham, "On some recent aspects of stochastic control and their applications", math.PR/0509711
- Dawn T. Robinson, "Control Theories in Sociology",
Annual
Review of Sociology
**33**(2007): 157--174 - Michael George Safonov, Stability and Robustness of Multivariable Feedback Systems
- Dragoslav D. Siljak, Decentralized Control of Complex Systems
- Jan C. Willems, Analysis of Feedback Systems