# Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization

arXiv: https://arxiv.org/abs/2504.04870 · HTML: https://mlsanity.com/paper/2504.04870/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach](https://mlsanity.com/paper/2511.09242/) (2025)
- [Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control](https://mlsanity.com/paper/2604.24663/) (2026)

## Abstract (arXiv)

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.