CUED IIB MEng Thesis

Author: Tom Lu

Supervisor: Guillaume Hennequin

The Koopman operator framework is becoming increasingly popular for obtaining linear representations of nonlinear systems from data. This project aims to optimally control input non-affine nonlinear systems, utilizing Deep Learning (DL) to discover the Koopman invariant subspace, bridging the gap between DL based Koopman eigenfunction discovery and optimal predictive control.

Script model/networks.py contains all networks discussed in the thesis, including:

LREN : Linearly Recurrent Encoder Network

DENIS: Deep Encoder with Initial State Parameterisation

DEINA: Deep Encoder for Input Non-Affine systems

LREN	DENIS	DEINA

Complete thesis and presentations and figures may be found in reports directory.

By lifting system state dimensions, system dynamics become globally linear, where LQR is readily applied. This technique is compared against the iterative LQR (iLQR). Video below shows our models controlling a pendulum it its vertical upright position.

Ours VS. iLQR	Effect of Latent Size (DENIS)

Left: Predicted trajectories overlaying ground truth. Right: Top two Koopman eigenfunctions magnitudes (which together, convey the Hamiltonian energy of the system).

Requires pytorch, python 3, numpy and matplotlib. To train the network, first configure a training json file inside training\configs. Then inside training directory, open terminal:

python trainer.py --config_dir PATH_TO_CONFIG --viz

This should locally initialize a model, trained with data specified in the configuration file.