# Data-Driven Optimal Control of Bilinear Systems

arXiv: https://arxiv.org/abs/2112.15510 · HTML: https://mlsanity.com/paper/2112.15510/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2021.

## Built on by (most cited first, 3 of 3)

- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)

## Abstract (arXiv)

This paper develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the system dynamics. Given an unknown bilinear system, we first characterize when the available data is suitable to solve the optimal control problem. This characterization leads us to propose an online control experiment design procedure that guarantees that any input/state trajectory can be represented as a linear combination of collected input/state data matrices. Leveraging this data-based representation, we transform the original optimal control problem into an equivalent data-based optimization problem with bilinear constraints. We solve the latter by iteratively employing a convex-concave procedure to convexify it and find a locally optimal control sequence. Simulations show that the performance of the proposed data-based approach is comparable with model-based methods.