  The paper presents a robust parameter learning methodology for identification
of nonlinear dynamical system from data while satisfying safety and stability
constraints in the context of learning from demonstration (LfD) methods.
Extreme Learning Machines (ELM) is used to approximate the system model, whose
parameters are learned subject to the safety and stability constraints obtained
using zeroing barrier and Lyapunov-based stability analysis in the presence of
model uncertainties and external disturbances. A constrained Quadratic Program
(QP) is developed, which accounts for the ELM function reconstruction error, to
estimate the ELM parameters. Furthermore, a robustness lemma is presented,
which proves that the learned system model guarantees safety and stability in
the presence of disturbances. The method is tested in simulations. Trajectory
reconstruction accuracy of the method is compared against state-of-the-art LfD
methods using swept error area (SEA) metric. Robustness of the learned model is
tested by conducting Monte Carlo tests. The proposed method is implemented on a
Baxter robot for a pick-and-place task where the robot is constrained to an
ellipsoidal safety region.
