Inferring Switched Nonlinear DynamicalSystems

Identification of dynamical and hybrid systems using trajectory data is an important way to construct models for complex systems where derivation from first principles is too difficult. In this paper, we study the identification problem for switched dynamical systems with polynomial ODEs. This is a difficult problem as it combines estimating coefficients for nonlinear dynamics and determining boundaries between modes. We propose two different algorithms for this problem, depending on whether to perform prior segmentation of trajectories. For methods with prior segmentation, we present a heuristic segmentation algorithm and a way to classify themodes using clustering. Formethods without prior segmentation, we extend identification techniques for piecewise affine models to our problem. To estimate derivatives along the given trajectories, we use Linear MultistepMethods. Finally, we propose a way to evaluate an identified model by computing a relative difference between the predicted and actual derivatives. Based on this evaluation method, we perform experiments on five switched dynamical systems with different parameters, for a total of twenty cases. We also compare with three baseline methods: clustering with DBSCAN, standard optimization methods in SciPy and identification of ARX models in Matlab, as well as with state-of-the-art identification method for piecewise affine models. The experiments show that our two methods perform better across a wide range of situations.