 This paper proposes a novel approach for learning a discrete-time dynamical system model from demonstration. It provides probabilistic guarantees on the safety and stability of the learned model by leveraging a combination of a discrete-time control barrier function and a discrete-time control Lyapunov function. Additionally, the proposed method uses a quadratically constrained quadratic program to estimate the extreme learning machine, ELM, parameters, which are then used to generate a model that can reproduce the demonstrations within a prescribed safe set while also ensuring stability and safety. Finally, simulations show that the learned model can adapt to changes in goal location without violating the safety and stability constraints. This article was authored by Aman Salihi, Tyler Taplan, and Ashwin P. Danny.