This course covers the learning outcomes and goals of understanding Koopman analysis, including Koopman observable subspaces, nonlinear dynamics, optimal control, compressed sensing, dynamic mode decomposition, Hankel alternative view of Koopman (HAVOK) analysis, magnetic field reversal, measles outbreaks, spectral analysis, and linear models for chaotic systems. The course teaches skills such as analyzing nonlinear dynamics, implementing optimal control strategies, conducting spectral analysis, and applying compressed sensing techniques. The teaching method includes lectures, demonstrations, and practical examples. The intended audience for this course is individuals interested in advanced topics in control theory, nonlinear dynamics, and spectral analysis.
Overview
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).
Taught by
Steve Brunton
