Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation
<|reference_start|>Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation: 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.<|reference_end|>
@article{xie2024data-driven,
    title={Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation},
    author={Yifan Xie and Julian Berberich and Frank Allg"ower},
    journal={arXiv preprint arXiv:2404.19096},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.19096},
    primaryClass={eess.SY cs.SY}
}