Data-Efficient Reinforcement Learning for Complex Nonlinear Systems.

Area of Science:

• Control Theory
• Machine Learning
• Dynamical Systems

Background:

• Complex nonlinear systems pose challenges for traditional control methods.
• Reinforcement learning (RL) offers a powerful framework for optimal control.
• Data efficiency is crucial for practical RL applications in real-world systems.

Purpose of the Study:

• To develop a data-efficient model-free reinforcement learning (RL) algorithm for nonlinear systems.
• To enable high-dimensional data-driven optimal control by lifting nonlinear dynamics into a linear model.
• To reduce the data requirements for learning optimal control strategies.

Main Methods:

• Utilizing Koopman operators to represent nonlinear dynamics in a linear framework.
• Employing a data-driven, model-based RL approach to derive an off-policy Bellman equation.
• Deducing a novel data-efficient RL algorithm that bypasses the need for an explicit Koopman-based linear model.
• Analyzing Koopman eigenfunctions for dataset truncation effects.

Main Results:

• The proposed algorithm achieves data-efficient optimal control for nonlinear systems.
• It effectively preserves essential dynamic information while minimizing data needs.
• The framework demonstrates successful validation on power system excitation control.
• Theoretical and numerical analyses confirm the efficacy of Koopman eigenfunctions in dataset truncation.

Conclusions:

• The developed model-free RL algorithm offers a significant advancement in controlling complex nonlinear systems efficiently.
• This approach reduces data dependency, making optimal control more accessible.
• The Koopman operator framework provides a robust method for analyzing and controlling nonlinear dynamics.
• The successful application to power systems highlights the practical utility of the proposed method.