Koopman Analysis

This course examines Koopman operator methods for representing and analyzing nonlinear dynamical systems. Topics include observable subspaces, optimal control, compressed sensing, dynamic mode decomposition, HAVOK analysis, chaotic systems, and Koopman spectral analysis.

Syllabus

Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control.
Koopman Observable Subspaces & Nonlinearization.
Koopman Operator Optimal Control.
Compressed Sensing and Dynamic Mode Decomposition.
Hankel Alternative View of Koopman (HAVOK) Analysis [FULL].
Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT].
Magnetic field reversal and Measles outbreaks: HAVOK models of chaos.
Linear model for chaotic Lorenz system [HAVOK].
Koopman Spectral Analysis (Control).
Koopman Spectral Analysis (Representations).
Koopman Spectral Analysis (Overview).
Koopman Spectral Analysis (Continuous Spectrum).
Koopman Spectral Analysis (Multiscale systems).