New MPC method guarantees stability with non-asymptotic learning bounds

This paper tackles a fundamental challenge in model predictive control: stabilizing systems when the dynamics are unknown and disturbances are present. The authors integrate online learning with robust tube MPC, a technique where a 'tube' of possible trajectories is maintained around a nominal reference. Instead of assuming a known uncertainty set, they use regularized least-squares to estimate parameters from data and derive a high-probability confidence ellipsoid. This uncertainty set is then used to tighten constraints and propagate the tube over a prediction horizon. The resulting formulation remains convex (linear and second-order cone constraints), making it computationally tractable.

The theoretical contribution is strong: they prove high-probability recursive feasibility (the optimization always finds a solution), robust constraint satisfaction (states stay within safe limits), and input-to-state stability (states converge to a bounded region). Unlike many learning-based MPCs that only provide asymptotic guarantees, this work gives explicit non-asymptotic state bounds. A numerical example with a simple linear system demonstrates the approach works in practice. For engineers, this means safer deployment of learning-based control in robotics, autonomous vehicles, and industrial process control where model uncertainty is unavoidable.