Calculus of Variations and Optimal Control Theory
Last update: 08 Dec 2024 00:00First version: 29 January 2023
Yet Another Inadequate Placeholder
Unsolicited and impertinent opinion: These are both bad names.
Confession of inadequacy: 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.)
For various Good Reasons, I am trying to write some deliberately-sloppy notes on these subjects; they've spun off into a separate notebook.
- See also:
- Control Theory
- Economics
- Large Deviations (in particular the works by [alphabetically] Dupuis and Ellis, by Eyink, and by Feng and Kurtz)
- Math I Ought to Learn
- Optimization
- Physics
- Recommended, big picture:
- Daniel Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction
- Enid R. Pinch, Optimal Control and the Calculus of Variations
- Martin L. Weitzman, Income, Wealth, and the Maximum Principle
- Recommended, close-ups:
- H. J. Kappen, "A linear theory for control of non-linear stochastic systems", Physical Review Letters 95 (2005): 200201, physics/0411119
- Recommended, these topics among many other things:
- V. I. Arnol'd, Mathematical Methods of Classical Mechanics
- Jürgen Jost, Postmodern Analysis [Nice treatment of calculus of variations, as part of a larger course on analysis]
- Recommended, I think:
- Herbert Goldstein, Classical Mechanics [This is what I learned calculus of variations from. But that was in the early 1990s, even before I began these notebooks, and I honestly have no idea now whether I'd recommend that.]
- To read:
- I. Gumowski and C. Mira, Optimization in Control Theory and Practice
- H. J. Kappen, "Path integrals and symmetry breaking for optimal control theory", Journal of Statistical Mechanics: Theory and Experiment (2005): P11011, physics/0505066
- Lanczos, The Variational Principles of Mechanics
- L. A. Pars, Introduction to the Calculus of Variations
- Daivd J. Toms, The Schwinger Action Principle and Effective Action
- Belinda Tzen, Anant Raj, Maxim Raginsky, Francis Bach, "Variational Principles for Mirror Descent and Mirror Langevin Dynamics", arxiv:2303.09532
