# Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems

arXiv: https://arxiv.org/abs/2504.08484 · HTML: https://mlsanity.com/paper/2504.08484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Smooth Strongly Convex Interpolation and Exact Worst-case Performance of First-order Methods](https://mlsanity.com/paper/1502.05666/) (2015)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [From noisy data to feedback controllers: non-conservative design via a matrix S-lemma](https://mlsanity.com/paper/2006.00870/) (2020)
- [Combining Prior Knowledge and Data for Robust Controller Design](https://mlsanity.com/paper/2009.05253/) (2020)
- [Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQR](https://mlsanity.com/paper/2401.14871/) (2024)
- [Set Membership identification of linear systems with guaranteed simulation accuracy](https://mlsanity.com/paper/2001.07628/) (2020)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [Data-driven Safe Control of Linear Systems Under Epistemic and Aleatory Uncertainties](https://mlsanity.com/paper/2202.04495/) (2022)
- [Interpolation Constraints for Computing Worst-Case Bounds in Performance Estimation Problems](https://mlsanity.com/paper/2309.12173/) (2023)
- [On the Sample Complexity of Set Membership Estimation for Linear Systems with Disturbances Bounded by Convex Sets](https://mlsanity.com/paper/2406.00574/) (2024)
- [Interpolation Conditions for Linear Operators and Applications to Performance Estimation Problems](https://mlsanity.com/paper/2302.08781/) (2023)
- [Controller Synthesis from Noisy-Input Noisy-Output Data](https://mlsanity.com/paper/2402.02588/) (2024)
- [Data-Driven Control of Positive Linear Systems using Linear Programming](https://mlsanity.com/paper/2303.12242/) (2023)
- [Controller synthesis for input-state data with measurement errors](https://mlsanity.com/paper/2402.04157/) (2024)

## Abstract (arXiv)

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design.