New MPC method guarantees stability under unbounded noise and constraints

Researchers from the University of Melbourne and ETH Zurich have tackled a critical challenge in learning-based control: ensuring stability when systems face both hard input constraints and unbounded stochastic noise. Their paper, submitted to arXiv on July 15, 2026, proposes a certainty-equivalence framework that blends model predictive control (MPC) with a saturated deadbeat controller, using online regularized least-squares (RLS) to estimate unknown dynamics. Unlike prior work that assumed bounded noise or asymptotic convergence, this work addresses the more realistic scenario of sub-Gaussian disturbances (e.g., heavy-tailed sensor noise).

The key theoretical contribution is the derivation of non-asymptotic, high-probability stability bounds for the closed-loop system. This means engineers can now compute explicit finite-time guarantees (e.g., “with 95% probability, the state stays within a set radius after 100 steps”) rather than relying on infinite-horizon asymptotic statements. The switching logic automatically selects between the MPC law and the deadbeat controller to prevent instability during learning. Numerical experiments demonstrate the bounds are tight, and the approach handles input saturation without sacrificing safety. This work opens the door to certifiable learning-based control for autonomous vehicles, robotics, and industrial process control where noise and constraints are unavoidable.