Active Learning of Switched Nonlinear Dynamical Systems

Most hybrid system identification methods rely on passive learning techniques, limiting theaccuracy of the learned model to the data at hand. We present an active learning approach to identify state-dependent switched nonlinear dynamical systems with polynomial ODEs. Counterexample trajectories indicating a divergence between the system under learning and a learned hypothesis model are provided by an approximate equivalence query. Segmentation is applied to the true trajectories of the counterexamples before treating each segment. We provide a way to incrementally update the learned continuous dynamics to accommodate each segment if needed, withoutany assumption on the number of modes, before updating the mode regions. Our method uses multivariate polynomial regression for finding the continuous dynamics and multinomial logistic regression for the mode regions. We illustrate our approach and its effectiveness on multiple examples, including a parametric one with 20 modes.