Learning Discrete-Time Uncertain Nonlinear Systems With Probabilistic Safety and Stability Constraints

This paper presents a discrete-time dynamical system model learning method from demonstration while providing probabilistic guarantees on the safety and stability of the learned model. The controlled dynamic model of a discrete-time system with a zero-mean Gaussian process noise is approximated using an Extreme Learning Machine (ELM) whose parameters are learned subject to chance constraints derived using a discrete-time control barrier function and discrete-time control Lyapunov function in the presence of the ELM reconstruction error. To estimate the ELM parameters a quadratically constrained quadratic program (QCQP) is developed subject to the constraints that are only required to be evaluated at sampled points. Simulations validate that the system model learned using the proposed method can reproduce the demonstrations inside a prescribed safe set while converging to the desired goal location starting from various different initial conditions inside the safe set. Furthermore, it is shown that the learned model can adapt to changes in goal location during reproductions without violating the stability and safety constraints.