# A trajectory-based framework for data-driven system analysis and control

arXiv: https://arxiv.org/abs/1903.10723 · HTML: https://mlsanity.com/paper/1903.10723/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations](https://mlsanity.com/paper/2311.05360/) (2023)
- [Assured Learning-enabled Autonomy: A Metacognitive Reinforcement Learning Framework](https://mlsanity.com/paper/2103.12558/) (2021)
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- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [Fading memory and the convolution theorem](https://mlsanity.com/paper/2408.07386/) (2024)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [A modular framework for stabilizing deep reinforcement learning control](https://mlsanity.com/paper/2304.03422/) (2023)
- [Data-Driven Adversarial Online Control for Unknown Linear Systems](https://mlsanity.com/paper/2308.08138/) (2023)
- [Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets](https://mlsanity.com/paper/2309.06658/) (2023)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2605.07052/) (2026)

## Abstract (arXiv)

The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven in the behavioral control framework, shows that a single measured trajectory can capture the full behavior of an LTI system and might therefore be used directly for system analysis and controller design, without explicitly identifying a model. In this paper, we translate the result from the behavioral context to the classical state-space control framework and we extend it to certain classes of nonlinear systems, which are linear in suitable input-output coordinates. Moreover, we show how this extension can be applied to the data-driven simulation problem, where we introduce kernel-methods to obtain a rich set of basis functions.