Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation

TL;DR

This paper introduces a robust, data-driven min-max MPC approach for unknown linear systems that accounts for noisy data, ensuring stability and constraints satisfaction, with an adaptive scheme to enhance performance using online data.

Contribution

It develops a novel min-max MPC framework based on noisy data, providing robustness guarantees and an adaptive scheme for improved control performance.

Findings

The method guarantees robust stability and constraint satisfaction.

The adaptive scheme improves closed-loop performance.

Numerical examples demonstrate effectiveness of the approach.

Abstract

Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods.