Learning-based Homothetic Tube MPC with Non-Asymptotic Guarantees
arXiv:2607.12343
The paper proposes a model predictive control method that builds a confidence set for unknown linear system parameters using regularized least‑squares, and incorporates this set into a homothetic tube MPC scheme with provable high‑probability feasibility and stability guarantees.
Abstract
This paper studies learning-based MPC for constrained stabilization of discrete-time linear systems with unknown system parameters and additive bounded disturbances. We develop a tractable homothetic-tube MPC scheme in which a high-probability parameter confidence set is generated from non-asymptotic regularized least-squares estimation, rather than assumed a priori. The resulting uncertainty set is embedded into robust tube propagation and constraint tightening, yielding a convex formulation with linear and second-order-cone constraints. We prove high-probability recursive feasibility, robust constraint satisfaction, and input-to-state stability, together with explicit non-asymptotic state bounds. A numerical example illustrates the effectiveness and theoretical guarantees.
16 pages, 2 figures