We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example.
@article{arxiv.2504.04870,
title = {Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization},
author = {Yifan Xie and Julian Berberich and Robin Strässer and Frank Allgöwer},
journal= {arXiv preprint arXiv:2504.04870},
year = {2025}
}