Data-Driven Min-Max MPC for Linear Systems

TL;DR

This paper introduces a data-driven min-max MPC approach for unknown linear systems that guarantees stability and constraint satisfaction by solving a semidefinite program based on noisy data.

Contribution

It proposes a novel data-driven min-max MPC scheme that handles noise and guarantees stability, robustness, and constraints for unknown LTI systems.

Findings

The optimization problem can be reformulated as a semidefinite program.

The control law stabilizes the system and satisfies constraints.

Numerical example confirms theoretical guarantees.

Abstract

Designing data-driven controllers in the presence of noise is an important research problem, in particular when guarantees on stability, robustness, and constraint satisfaction are desired. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme to design state-feedback controllers from noisy data for unknown linear time-invariant (LTI) system. The considered min-max problem minimizes the worst-case cost over the set of system matrices consistent with the data. We show that the resulting optimization problem can be reformulated as a semidefinite program (SDP). By solving the SDP, we obtain a state-feedback control law that stabilizes the closed-loop system and guarantees input and state constraint satisfaction. A numerical example demonstrates the validity of our theoretical results.