Dynamical system learning using extreme learning machines with safety and stability guarantees

Abstract

SummaryThis article presents a continuous dynamical system model learning methodology that can be used to generate reference trajectories for the autonomous systems to follow, such that these trajectories are invariant to a given closed set and uniformly ultimately bounded with respect to an equilibrium point inside the closed set. The autonomous system dynamics are approximated using extreme learning machines (ELM), the parameters of which are learned subject to the safety constraints expressed using a reciprocal barrier function, and the stability constraints derived using a Lyapunov analysis in the presence of the ELM reconstruction error. This formulation leads to solving a constrained quadratic program (QP) that includes a finite number of decision variables with an infinite number of constraints. Theorems are developed to relax the QP with infinite number of constraints to a QP with a finite number of constraints which can be practically implemented using a QP solver. In addition, an active sampling methodology is developed that further reduced the number of required constraints for the QP by only evaluating the constraints at a smaller subset of points. The proposed method is validated using a motion reproduction task on a seven degree‐of‐freedom Baxter robot, where the task space position and velocity dynamics are learned using the presented methodology.