Estimation of region of attraction with Gaussian process classification

Abstract

This paper proposes a methodology for assessing the region of attraction (ROA) of stable equilibrium points, a challenging problem for a general nonlinear system, using binary Gaussian process classification (GPC). Interest in this method stems from the fact that an arbitrary point belonging to the system’s state space can be classified in the region of attraction or not. Importantly the proposed GPC approach for determining ROA gives a minimum confidence level associated with the estimate. Moreover, the active learning scheme helps to update the GPC model and yield better predictions by selecting informative observations from the state space sequentially. The methodology is applied to several examples to illustrate the effectiveness of this approach.