Non-asymptotic Bounds of Learning-based Linear MPC With Input Constraints and Unbounded Stochastic Noise

This paper studies learning-based model predictive control (MPC) for stabilizing unknown discrete-time linear systems with hard input constraints and additive unbounded sub-Gaussian disturbances. We adopt a certainty-equivalence (CE) design that combines a switching MPC control law with online regularized least-squares (RLS) parameter estimation. The resulting switching control law blends the MPC with a saturated deadbeat controller, ensuring global closed-loop stability. Building upon non-asymptotic error bound of least-squares, we derive non-asymptotic, high-probability stability bounds for the closed-loop system under the proposed switching controller. Numerical experiments illustrate and support the theoretical findings.