# End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

arXiv: https://arxiv.org/abs/2409.18010 · HTML: https://mlsanity.com/paper/2409.18010/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 73 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 27 of 27)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Koopman Operator Dynamical Models: Learning, Analysis and Control](https://mlsanity.com/paper/2102.02522/) (2021)
- [Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2002.08538/) (2020)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [A Tutorial on Concentration Bounds for System Identification](https://mlsanity.com/paper/1906.11395/) (2019)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [Finite Sample Identification of Bilinear Dynamical Systems](https://mlsanity.com/paper/2208.13915/) (2022)
- [From noisy data to feedback controllers: non-conservative design via a matrix S-lemma](https://mlsanity.com/paper/2006.00870/) (2020)
- [Learning to Control Linear Systems can be Hard](https://mlsanity.com/paper/2205.14035/) (2022)
- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Koopman-based feedback design with stability guarantees](https://mlsanity.com/paper/2312.01441/) (2023)
- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [Feedback Stabilization Using Koopman Operator](https://mlsanity.com/paper/1810.00089/) (2018)
- [Behavioral Theory for Stochastic Systems? A Data-driven Journey from Willems to Wiener and Back Again](https://mlsanity.com/paper/2209.06414/) (2022)
- [Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey](https://mlsanity.com/paper/2306.16042/) (2023)
- [Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control](https://mlsanity.com/paper/2309.04074/) (2023)
- [A structure exploiting SDP solver for robust controller synthesis](https://mlsanity.com/paper/2304.05037/) (2023)
- [Input-to-State Stability in Probability](https://mlsanity.com/paper/2304.14578/) (2023)
- [Direct data-driven LPV control of nonlinear systems: An experimental result](https://mlsanity.com/paper/2211.17191/) (2022)
- [Control of bilinear systems using gain-scheduling: Stability and performance guarantees](https://mlsanity.com/paper/2304.04486/) (2023)

## Built on by (most cited first, 1 of 1)

- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)

## Abstract (arXiv)

In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.