The linear–quadratic regulator and Koopman Observable Subspaces

This repository contains two notebooks illustrating the linear–quadratic regulator and the idea behind the Koopman operator.

Part I gives the intuitions for the linear–quadratic regulator framework and solves for the optimal controller in Python. Part II introduces the Koopman operator and discusses how a new (better) controller can be obtained compared to Part I.

Acknowledgements

• The linear system studied in this notebook is based on the paper: Brunton, Steven L., et al. "Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control." PloS one 11.2 (2016). For details and more references, I strongly invite you to read it.
• A video summarizing the paper can be found here: https://www.youtube.com/watch?v=qOdwRel-1xA&list=PLMrJAkhIeNNSVXUvppZTYNHKQUD-oWys9&index=3)