Learning Dynamical Systems using Local Stability Priors
This work addresses the challenge of system identification in control and robotics by improving accuracy and efficiency, though it is incremental as it builds on existing stability-based methods.
The paper tackled the problem of learning dynamical systems by incorporating local stability priors to simultaneously estimate the vector field and region of attraction from trajectories, resulting in efficient sampling and accurate dynamics estimation within an inner approximation of the region.
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system 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 plays an experiment design role 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. Numerical 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.