Decision Tree Models of Continuous Systems

Cyber-Physical Systems (CPS) are often black-box systems, i.e., knowledge of the inner workings or a system model is not available. Nevertheless, models of CPS are needed for various tasks, ranging from verification, over testing to monitoring at runtime. For these tasks, finite and discrete models facilitating understandability, compactness, and efficiency are often desirable. Deriving a discrete model of a continuous-valued CPS is difficult. A simple abstraction is achieved with a time and value discretization through sampling and discretization intervals. We consider observing the system with bounded history and apply decision tree learning on discretized observations to generate a model of the system. The model supports the identification of system characteristics and predicts a valid next output based on the bounded history. We prove an upper bound on the error size for the prediction of an output. Experimental results give practical insight and present a comparison to automata learning.