Learning Dynamical Systems Using Local Stability Priors

Abstract

A computational approach to simultaneously learn the vector field of a dynamical system with a locally asymptotically stable equilibrium and its region of attraction from the system's trajectories is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction can be used to design experiments by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Simulation results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.