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

Robust Learning of Nonlinear Dynamical Systems with Safety and Stability Properties