Identifying Causal Structure in Dynamical Systems

arXiv (Cornell University)

Abstract

Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their limits. Data-driven methods provide an alternative. However, without structural knowledge, these methods are prone to finding spurious correlations in the training data, which can hamper generalization capabilities of the obtained models. This can significantly lower control and prediction performance when the system is exposed to unknown situations. A preceding causal identification can prevent this pitfall. In this paper, we propose a method that identifies the causal structure of control systems. We design experiments based on the concept of controllability, which provides a systematic way to compute input trajectories that steer the system to specific regions in its state space. We then analyze the resulting data leveraging powerful techniques from causal inference and extend them to control systems. Further, we derive conditions that guarantee the discovery of the true causal structure of the system. Experiments on a robot arm demonstrate reliable causal identification from real-world data and enhanced generalization capabilities.

Authors 4

1. Dominik Baumann

   Uppsala University

   Affiliation as printed

   Department of Information Technology Uppsala University Uppsala , Sweden

2. Friedrich Solowjow Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering RWTH Aachen University Aachen , Germany

3. Karl Henrik Johansson

   KTH Royal Institute of Technology

   Affiliation as printed

   Division of Decision and Control Systems and Digital Futures KTH Royal Institute of Technology Stockholm , Sweden

4. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering RWTH Aachen University Aachen , Germany