Things change, this is the defining characteristic of life. The dynamics of the world seek to be understood and sometimes even controlled, yielding the complementary fields of dynamical systems and control theory. This is the community gym of applied math, with arenas for all kinds of things like functional analysis (operator semigroups and stuff), optimization & ML (regret bounds and optimal control), geometry (invariant/attractive structures, dimension theory), and measure theory (probability, random systems, ergodicity).
Topics hopefully include:
- stability, controllability
- invariant sets and attractive structures
- dimension theory
- control theory
- ODEs and PDEs, from a dynamical pov
list of papers
- [x] "Spectral State Space Models" - Naman, Daniel, Xinyi, Hazan
- [ ] "Markov Chains and Dynamical Systems: The Open System Point of View" - Stephane Attal
- [ ] Tensor Decompositions Meet Control Theory:
Learning General Mixtures of Linear Dynamical Systems — Ankur Moitra et al
- [x] "Learning Linear Dynamical Systems via Spectral Filtering" - Hazan, Karan, Cyril
- [ ] "Boosting for Control of Dynamical Systems" - Naman, Nataly, Hazan, Zhou
- [ ] "From repeated to continuous quantum interactions" - Attal and Pautrat
- [ ] "Iterated Function Systems: A Comprehensive Survey" - Ghosh and Marecek
- [ ] "Maximum Principle Based Algorithms for Deep Learning" - Ed Weinan et al
- [ ] "Observing Infinite-Dimensional Dynamical Systems" - Jessica Lin & William Ott
- [ ] "Online Control For Adaptive Tapering Of Medications" - Paula & Ben Recht
- [x] “Online Control of Unknown Time-Varying Dynamical Systems" - Edgar, Paula, Max, Hazan
- [x] "Linearization in the large of nonlinear systems and Koopman operator spectrum" - Lan, Mezic
- [x] "Introduction to Online Nonstochastic Control" - Hazan & Karan