Machine Learning Koopman Operator Theory Analytical Backpropogation Data Science Data Driven Modeling Imitation Learning Linear Quadratic Regulator
Abstract:
Data driven modeling and machine learning methods have been becoming increasingly popular for learning the control of dynamic systems. Due to the typically nonlinear nature of most experimentally produced dynamic systems, Koopman Operator Theory can be used in order to find a higher-dimensional linearized model for the aforementioned nonlinear system. One of the biggest problems with using Koopman Operator Theory to model dynamic systems is that learning the many parameters required for state transitions between Real and Koopman Eigenspaces require complicated, multi-step algorithms. Due to this, traditional backpropogation for finding parameter gradients becomes too computationally expensive, and in some cases unfeasible. This thesis provides an efficient method for analytically computing parameter gradients using an adjoint-based approach. The adjoint-based approach was successful for imitation learning of a system governed by a Linear Quadratic Regulator, and in linearizing a parabolic nonlinear system using Koopman Operator Theory.
