The approach aims to handle diverse systems, to include system knowledge and to result in an easily interpretable model.

Section \[sec:stateOfTheArt\] will cover basic theory regarding system identification and current approaches. A new concept is presented in Section \[sec:Concept\]. Part \[sec:practicalEvaluation\] contains the practical experiments and their results while Part \[sec:discussion\] gives a deepening discussion. Section \[sec:conclusion\] summarizes the findings and gives a brief outlook to further applications.

State of the art {#sec:stateOfTheArt}
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Whenever a certain degree of precision is required for tasks like optimization or anomaly detection, simple dynamic models may deviate too much from the actual system, especially in the critical regions of hysteretic systems, where the state transitions happen. In order to pursue model-based approaches for these tasks, sophisticated models are required.

System Identification for nonlinear hybrid systems
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### Hybrid systems.

The considered type of dynamic systems contains both discrete and continuous parts. Depending on a discrete state, a different behavior is observed. A famous example is the temperature characteristics of water: the behavior changes with reaching the threshold of 100 $^\circ C$ due to the phase transition. Therefore, it makes sense to create two distinct models: one for the discrete state “temperature below 100 