Framework for Synthesis of Hybrid Automata from Time Series with Time- or State-Dependent Switching Conditions

Hansen, Jakob Østenkjær ; Kristensen, Alex Immerkær

4. term

Software, Master

2023

2023-06-08

22 pages

A hybrid automaton is an appropriate mathematical formalism for modelling systems with mixed discrete and continuous dynamics. The hybrid automaton combines discrete control graphs with continuous dynamics defined by differential equations. In this paper, we introduce an offline learning algorithm to automatically synthesise a hybrid automaton from time series. The algorithm consists of several procedures, including segmentation of time series, structure learning, and discovery of both dynamics and conditions. We present a novel method for determining the conditions of a model learned from stationary time series, as well as a new time-based method for models learned from time series that exhibit trends. The evaluation shows that the algorithm can learn simple models with an accurate graph structure and appropriate dynamics from stationary time series using variable conditions, as well as from non-stationary time series exhibiting trends using the timed conditions. However, the results show poor performance if the change point detection algorithm is unable to accurately segment the time series, or if the location dynamics are indistinguishable. Indistinguishable dynamics between locations may cause the change point detection to misidentify segments, and it may result in the structure learning procedure being unable to identify the locations as well as to associate the segments to locations.

A hybrid automaton is an appropriate mathematical formalism for modelling systems with mixed discrete and continuous dynamics. The hybrid automaton combines discrete control graphs with continuous dynamics defined by differential equations. In this paper, we introduce an offline learning algorithm to automatically synthesise a hybrid automaton from time series. The algorithm consists of several procedures, including segmentation of time series, structure learning, and discovery of both dynamics and conditions. We present a novel method for determining the conditions of a model learned from stationary time series, as well as a new time-based method for models learned from time series that exhibit trends. The evaluation shows that the algorithm can learn simple models with an accurate graph structure and appropriate dynamics from stationary time series using variable conditions, as well as from non-stationary time series exhibiting trends using the timed conditions. However, the results show poor performance if the change point detection algorithm is unable to accurately segment the time series, or if the location dynamics are indistinguishable. Indistinguishable dynamics between locations may cause the change point detection to misidentify segments, and it may result in the structure learning procedure being unable to identify the locations as well as to associate the segments to locations.

Hybrid Automata ; Synthesis ; Framework ; Time Series ; Timed Conditions ; Structure Learning ; Continuous Dynamics

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