Sparse Identification for Non-linear Dynamics applied to hysteresis-controlled systems

Hysteresis-controlled devices are widely used in industrial applications. For example, cooling devices usually contain a two-point controller, resulting in a nonlinear hybrid system with two discrete states. Behavior models of dynamic systems are essential for optimizing such industrial supply technology. However, conventional system identification approaches cannot handle hysteresis-controlled devices. Thus, a new identification method called Sparse Identification of Nonlinear Dynamics (SINDy) is extended to handle hybrid systems. In this new method (SINDyHyrid), tailored basis functions in form of relay hysterons are added to the library which is used by SINDy. Experiments with a hysteresis controlled water basin show that this approach correctly identifies state transitions of hybrid systems and also succeeds in modeling the dynamics of the discrete system states. A novel proximity hysteron gains the robustness of this method. The impacts of the sampling rate and the signal noise ration of the measurement data are examined accordingly.