A Risk-Aware Adaptive Robust MPC with Learned Uncertainty Quantification

Abstract: Solving chance-constrained optimal control problems for systems subject to non-stationary uncertainties is a significant challenge.Conventional robust model predictive control (MPC) often yields excessive conservatism by relying on static worst-case assumptions, while standard stochastic MPC methods struggle when underlying uncertainty distributions are unknown a priori.This article presents a Risk-Aware Adaptive Robust MPC (RAAR-MPC) framework,a hierarchical architecture that systematically orchestrates a novel synthesis of proactive, learning-based risk assessment and reactive risk regulation. The framework employs a medium-frequency risk assessment engine, which leverages Gaussian process regression and active learning, to construct a tight, data-driven characterization of the prediction error set from operational data.Concurrently, a low-timescale outer loop implements a self-correcting update law for an adaptive safety margin to precisely regulate the empirical risk and compensate for unmodeled dynamics.This dual-timescale adaptation enables the system to rigorously satisfy chance constraints with a user-defined probability, while minimizing the conservatism inherent in traditional approaches.We formally establish that the interplay between these adaptive components guarantees recursive feasibility and ensures the closed-loop system satisfies the chance constraints up to a user-defined risk level with high probability.Numerical experiments on a benchmark DC-DC converter under non-stationary parametric uncertainties demonstrate that our framework precisely achieves the target risk level, resulting in a significantly lower average cost compared to state-of-the-art robust and stochastic MPC strategies.