Model-Free Disturbance Observer with Online Modification: Listening to MFDOOM

Jul 16, 2026

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Data-Enabled Predictive Control (DeePC) enables controlling unknown systems using input-output data, but its closed-loop quality depends on how representative the collected data remain under disturbances, which inevitably induce prediction errors. The paper introduces an augmentation of DeePC based on Model-Free Disturbance Observer with Online Modification (MFDOOM). MFDOOM continuously updates a dedicated Hankel matrix of past prediction errors to correct output predictions. Theoretical analysis and simulations compare MFDOOM with other time-varying DeePC algorithms and show reduced tracking error and less online-update burden for disturbances generated by autonomous LTI output dynamics.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

Introduction

Preliminaries

Notations

Behavioral System Theory

Problem Formulation

MFDOOM Method

Simulation Results

Conclusion

Model-Free Disturbance Observer with Online Modification: Listening to MFDOOM Nadav Barak ∗ Christian Grussler ∗∗ ∗ Technion – Israel Institute of Technology, Faculty of Mechanical Engineering, Haifa 3200003 Israel (e-mail: [nadav.barak@campus.technion.ac.il](nadav.barak@campus.technion.ac.il)).∗∗ Technion – Israel Institute of Technology, The Stephen B. Klein Faculty of Aerospace Engineering, Haifa 3200003 Israel (e-mail: [cgrussler@technion.ac.il](cgrussler@technion.ac.il)) .OC] 8 Jul 2026 Abstract: Data-Enabled Predictive Control (DeePC) has recently emerged as a framework for controlling unknown systems from data. However, its performance relies on the relevance of the collected data, and as such, disturbances lead to inevitable errors. This paper addresses this problem by proposing an augmentation of DeePC using Model-Free Disturbance Observer with Online Modification (MFDOOM) . The method corrects output predictions based on previous prediction errors using a dedicated continuously updated Hankel matrix. We compare our method, both theoretically and through simulation, to other recent algorithms designed for time-varying systems in the DeePC framework. It is shown that for disturbances that can be modeled as the output of an autonomous linear time-invariant system, this approach can reduce tracking error and online-update burden compared with existing online DeePC variants. Keywords: Data-Enabled Predictive Control, Autonomous Systems, Disturbance Observer 1. INTRODUCTION MPC ODeePC MDeePC MFDOOM arXiv :2607 .07082v1 2021; Huang et al., 2021a, 2023; Zieglmeier et al., 2025) . Rather than using an explicit model, DeePC predicts future behavior using Hankel matrices constructed from input-output data (Coulson et al., 2019) . Because unmodeled or insufficiently represented dynamics can degrade performance, regularization has been proposed to improve robustness, particularly for nonlinear or linear time-varying (LTV) systems (Coulson et al., 2019) . Related online variants include Online DeePC (ODeePC), which refreshes the Hankel matrices with new measurements (Baros et al., 2022), and Online Reduced-Order DeePC, here referred to as MDeePC, which updates a mosaic Hankel matrix only when new trajectories enrich the implicit model (Vahidi-Moghaddam et al., 2025) . When disturbances are generated by an autonomous linear system, e.g., sinusoids, they effectively alter the measured plant behavior. Since such disturbances may appear or disappear, the resulting prediction error is time-varying. As a result, standard DeePC may under perform, while conservative regularization can degrade nominal tracking (Huang et al., 2021b) . Modifying the nominal behavior matrices (i.e. ODeePC) or expanding them (MDeePC) partially address this issue, but coupling disturbance adaptation to the baseline predictor results in several drawbacks, such as needless noise injection or increased online computation. 0 2 4 6 8 10 12 14 Time [s] Fig. 1. Simulated output response of an undisturbed (12) controlled by MPC, compared to ODeePC, MDeePCand MFDOOM controlling the same system under disturbance (shaded region) . This paper introduces the Model-Free Disturbance Observer with Online Modification (MFDOOM), a model-free correction mechanism for autonomous LTV disturbances (ALTVDs) . MFDOOM compares DeePC predictions with measured outputs and maintains a continuously updated Hankel matrix of prediction errors, which implicitly models the error dynamics for future compensation. Unlike methods that update the nominal behavior matrices, MFDOOM keeps the baseline DeePC predictor fixed and adapts only the correction mechanism. As illustrated in Figure 1, this enables improved tracking under sinusoidal disturbances while requiring less real-time data updating than existing online DeePC variants. The remainder of the paper is organized as follows. Section 2 introduces preliminaries, Section 3 states the problem and elaborates on

FAQs

What limitation of DeePC motivates MFDOOM?

DeePC performance depends on the relevance of collected data, and disturbances cause time-varying prediction errors that can degrade tracking.

How does MFDOOM modify DeePC predictions?

MFDOOM keeps the baseline DeePC predictor fixed and updates a dedicated Hankel matrix using previous prediction errors, which implicitly models error dynamics for future compensation.

Against what approaches is MFDOOM compared, and what benefits are reported?

The method is compared theoretically and via simulation to recent DeePC variants for time-varying systems; for disturbances modeled as outputs of autonomous LTI dynamics, MFDOOM reduces tracking error and online-update burden.

Jul 16, 2026

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