Identification of hybrid systems with dynamics-based modeling through symbolic regression

Hybrid systems combine both continuous and discrete behavior. These systems serve as models in many fields, including control systems, robotics, and industrial processes. However, due to their complexity, finding an accurate model is a challenge. This paper presents a holistic approach to learning models of hybrid systems using symbolic regression. Our method leverages symbolic regression to automatically discover accurate and interpretable mathematical models in the form of hybrid systems from observed data. An advantage of our algorithm is that it detects transitions between different behavioral modes of a system based on the inherent dynamics. From learned expressions for the dynamical behavior of a system, we form a hybrid system by combining the learned expressions with a decision tree determining the current behavioral mode from data. This hybrid decision tree serves regression, prediction, and further related tasks. Our results demonstrate that symbolic regression can effectively identify the underlying dynamics of a real hybrid system and predict output signals on new input data with high accuracy. • Hybrid systems are powerful models combining continuous and discrete dynamics. • A data-driven identification automates model generation. • Often, dynamic modes are identified from signal similarities. • Different initial conditions lead to dissimilar signals even for same dynamics. • Dynamics-based identification is a more effective approach.