Non-asymptotic Bounds of Learning-based Linear MPC With Input Constraints and Unbounded Stochastic Noise
arXiv:2607.13513
The paper proposes a certainty‑equivalence, switching model predictive control scheme that learns unknown linear dynamics online via regularized least‑squares, handling hard input constraints and unbounded sub‑Gaussian noise, and provides non‑asymptotic high‑probability stability guarantees.
Abstract
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.
16 pages, 1 figure