Deep Learning of Koopman Representation for Control

TL;DR

This paper introduces a data-driven, model-free control method using deep neural networks to learn Koopman operators, enabling linear control of nonlinear systems without prior domain knowledge.

Contribution

It develops a novel approach combining deep learning and Koopman theory for control, bypassing the need for explicit system models or domain expertise.

Findings

Successfully applied to classic dynamical systems in OpenAI Gym

Demonstrates effective control without prior system models

Uses reinforcement learning for data collection and Koopman learning

Abstract

We develop a data-driven, model-free approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator for the purpose of control. In particular, DNN is employed for the data-driven identification of basis function used in the linear lifting of nonlinear control system dynamics. The controller synthesis is purely data-driven and does not rely on a priori domain knowledge. The OpenAI Gym environment, employed for Reinforcement Learning-based control design, is used for data generation and learning of Koopman operator in control setting. The method is applied to two classic dynamical systems on OpenAI Gym environment to demonstrate the capability.