Safe Learning MPC With Limited Model Knowledge and Data

This article presents an end-to-end framework for safe learning-based control (LbC) using nonlinear stochastic MPC and distributionally robust optimization (DRO). This work is motivated by several open challenges in LbC literature. Many control-theoretic LbC methods require subject matter expertise (SME), often manifested as preexisting data of safe trajectories or structural model knowledge, to translate their own safety guarantees. In this article, we focus on LbC where the controller is applied directly to a system of which it has no or extremely limited direct experience, toward safety during tabula-rasa or “ blank slate ” model-based learning and control as a challenging case for validation. This explores the boundary of the status quo in control theory relating to requirements for SME. We show under basic and limited assumptions on the underlying problem, we can translate probabilistic guarantees on the feasibility of nonlinear systems using results in stochastic MPC and DRO literature whose relevance we formally extend in mathematical analysis. We also present a coupled and intuitive formulation for the persistence of excitation (PoE) and illustrate the connection between PoE and the applicability of the proposed method. Our case studies of vehicle obstacle avoidance and safe extremely fast charging of lithium-ion batteries reveal powerful empirical results supporting the underlying theory.