publications

Preprints

1. Informativity for Data-driven Prediction

   Joel Stevens and Jeremy Coulson

   2026

   Abstract arXiv

   In this work we examine the problem of data-driven prediction. That is, given a LTI system with unknown dynamics, we wish to use data collected from the system to predict the system’s output response to a given sequence of known inputs. Current methods for predicting require strong conditions on the data such as persistency of excitation. We examine this problem with the goal of finding weaker conditions that still enable prediction. We approach the problem from the data informativity perspective and formally define the notion of informativity for unique prediction. We provide sufficient conditions for informativity for unique prediction and design algorithms to compute the unique output trajectory of the unknown system given known inputs. We demonstrate the results with a numerical example showing that unique output prediction is possible without being able to uniquely identify the unknown data-generating system.

2. Min-Max Grassmannian Optimization for Online Subspace Tracking

   Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran, Alberto Padoan, Jeremy Coulson, and Ravi Banavar

   2026

   Abstract arXiv

   This paper discusses robustness guarantees for online tracking of time-varying subspaces from noisy data. Building on recent work in optimization over a Grassmannian manifold, we introduce a new approach for robust subspace tracking by modeling data uncertainty in a Grassmannian ball. The robust subspace tracking problem is cast into a min-max optimization framework, for which we derive a closed-form solution for the worst-case subspace, enabling a geometric robustness adjustment that is both analytically tractable and computationally efficient, unlike iterative convex relaxations. The resulting algorithm, GeRoST (Geometrically Robust Subspace Tracking), is validated on two case studies: tracking a linear time-varying system and online foreground-background separation in video.

3. On the Sensitivity of the Subspace Predictor to Behavioral Perturbations

   Dian Jin and Jeremy Coulson

   2026

   Abstract arXiv

   Behavioral systems define discrete-time Linear Time-Invariant systems in terms of a set of trajectories, which forms a linear subspace. This subspace underlies the subspace predictor used in data-driven prediction and control. In practice, such subspaces are typically represented through data matrices. For robustness certification and uncertainty quantification, however, these matrix representations are coordinate-dependent and therefore do not provide a coordinate-free way to quantify uncertainty. In this work, we establish two key properties of the subspace predictor. We first show that the subspace predictor is invariant under change of basis and depends only on the underlying behavioral subspace. We then derive the first explicit prediction error bound in terms of behavioral distance between the true subspace and an estimate, showing that the predictor is locally Lipschitz with respect to behavioral perturbations. We also present a one-step prediction error bound that is relevant for receding-horizon implementations and can be computed directly. Numerical experiments show that the theoretical bound upper-bounds the prediction error, and that the average prediction error bound grows linearly with the behavioral distance.

4. From Time Series to Dissipativity of Linear Systems with Dynamic Supply Rates

   2026

   Abstract arXiv

   This paper studies the problem of verifying dissipativity of linear time-invariant (LTI) systems using input-output data. We leverage behavioral systems theory to express dissipativity in terms of quadratic difference forms (QDFs), allowing the study of general dynamic quadratic supply rates. We work under the assumptions that the data-generating system is controllable, and an upper bound is given on its lag. As our main results, we provide sufficient conditions for the data to be informative for dissipativity. We also show that for a specific class of static supply rates, these conditions are both necessary and sufficient. For the latter supply rates, it turns out that certification of dissipativity is only possible from data that enable unique system identification. As auxiliary results, we highlight some properties of QDFs, such as upper bounds on the degree of storage functions.

5. Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach

   Shreyas Bharadwaj, Bamdev Mishra, Cyrus Mostajeran, Alberto Padoan, Jeremy Coulson, and Ravi N. Banavar

   2025

   Abstract arXiv

   The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate subspace inclusion between measured and true data spaces. The uncertainty in this geometric relation is modeled as a metric ball on the Grassmannian manifold, leading to a min-max problem over Euclidean and manifold variables. The inner maximization admits a closed-form solution, enabling an efficient algorithm with a transparent geometric interpretation. Applied to robust finite-horizon linear-quadratic tracking in data-enabled predictive control, the method improves upon existing robust least-squares formulations, achieving stronger robustness and favorable scaling under small uncertainty.

6. Online Subspace Learning on Flag Manifolds for System Identification

   Dian Jin and Jeremy Coulson

   2025

   Abstract arXiv

   Data-driven control methods based on subspace representations are powerful but are often limited to linear time-invariant systems where the model order is known. A key challenge is developing online data-driven control algorithms for time-varying systems, especially when the system’s complexity is unknown or changes over time. To address this, we propose a novel online subspace learning framework that operates on flag manifolds. Our algorithm leverages streaming data to recursively track an ensemble of nested subspaces, allowing it to adapt to varying system dimensions without prior knowledge of the true model order. We show that our algorithm is a generalization of the Grassmannian Recursive Algorithm for Tracking. The learned subspace models are then integrated into a data-driven simulation framework to perform prediction for unknown dynamical systems. The effectiveness of this approach is demonstrated through a case study where the proposed adaptive predictor successfully handles abrupt changes in system dynamics and outperforms several baselines.

Journal Papers

1. Distances Between Finite-Horizon Linear Behaviors

   Alberto Padoan and Jeremy Coulson

   IEEE Control Systems Letters, 2025

   Abstract Link arXiv

   The letter introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain invariant under coordinate changes, rotations, and permutations, ensuring independence from input-output partitions. Moreover, they naturally encode complexity-misfit trade-offs for Linear Time-Invariant (LTI) behaviors, providing a principled solution to a longstanding puzzle in behavioral systems theory. The resulting framework characterizes modeling as a minimum distance problem, identifying the Most Powerful Unfalsified Model (MPUM) as optimal among all systems unfalsified by a given dataset. Finally, we illustrate the value of these metrics in a time-series anomaly detection task, where their finer resolution yields superior performance over existing distances.

2. Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations

   Florian Dörfler, Jeremy Coulson, and Ivan Markovsky

   IEEE Transactions on Automatic Control, 2023

   Abstract Link arXiv

   In this article, we discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal decision compatible with recorded data assembled in a Hankel matrix and robustified through suitable regularizations. We formulate these two problems in the language of behavioral systems theory and parametric mathematical programs, and we bridge them through a multicriteria formulation trading off system identification and control objectives. We illustrate our results with two methods from subspace identification and control: namely, subspace predictive control and low-rank approximation, which constrain trajectories to be consistent with a nonparametric predictor derived from (respectively, the column span of) a data Hankel matrix. In both cases, we conclude that direct and regularized data-driven control can be derived as convex relaxation of the indirect approach, and the regularizations account for an implicit identification step. Our analysis further reveals a novel regularizer and a plausible hypothesis explaining the remarkable empirical performance of direct methods on nonlinear systems.

3. A Quantitative Notion of Persistency of Excitation and the Robust Fundamental Lemma

   IEEE Control Systems Letters, 2023

   Abstract Link

   The fundamental lemma by Willems and coauthors enables a parameterization of all trajectories of a linear time-invariant system in terms of a single, measured one. This result plays a key role in data-driven simulation and control. The fundamental lemma relies on a persistently exciting input to the system to ensure that the Hankel matrix of resulting input/output data has the “right” rank, meaning that its columns span the entire subspace of trajectories. However, such binary rank conditions are known to be fragile in the sense that a small additive noise could already cause the Hankel matrix to have full rank. In this letter we present a robust version of the fundamental lemma. The idea behind the approach is to guarantee certain lower bounds on the singular values of the data Hankel matrix, rather than qualitative rank conditions. This is achieved by designing the inputs of the experiment such that the minimum singular value of an input Hankel matrix is sufficiently large, inspiring a quantitative notion of persistency of excitation. We highlight the relevance of the result in a data-driven control case study by comparing the predictive control performance for varying degrees of persistently exciting data.

4. Distributionally Robust Chance Constrained Data-Enabled Predictive Control

   Jeremy Coulson, John Lygeros, and Florian Dörfler

   IEEE Transactions on Automatic Control, 2022

   Abstract Link arXiv

   In this article we study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant (LTI) systems, which is the key ingredient of a predictive control algorithm—albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on 1) a nonparametric representation of the subspace spanning the system behavior, where past trajectories are sorted in Page or Hankel matrices; and 2) a distributionally robust optimization formulation which gives rise to strong probabilistic performance guarantees. We show that for certain objective functions, DeePC exhibits strong out-of-sample performance, and at the same time respects constraints with high probability. The algorithm provides an end-to-end approach to control design for unknown stochastic LTI systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study.

5. Decentralized Data-Enabled Predictive Control for Power System Oscillation Damping

   Linbin Huang, Jeremy Coulson, John Lygeros, and Florian Dörfler

   IEEE Transactions on Control Systems Technology, 2022

   Abstract Link arXiv

   We employ a novel data-enabled predictive control (DeePC) algorithm in voltage source converter (VSC)-based high-voltage DC (HVDC) stations to perform safe and optimal wide-area control for power system oscillation damping. Conventional optimal wide-area control is model based. However, in practice, detailed and accurate parametric power system models are rarely available. In contrast, the DeePC algorithm uses only input-output data measured from the unknown system to predict the future trajectories and calculate the optimal control policy. We showcase that the DeePC algorithm can effectively attenuate interarea oscillations even in the presence of measurement noise, communication delays, nonlinear loads, and uncertain load fluctuations. We investigate the performance under different matrix structures as data-driven predictors. Furthermore, we derive a novel Min-Max DeePC algorithm to be applied independently in multiple VSC-HVDC stations to mitigate interarea oscillations, which enables decentralized and robust optimal wide-area control. Further, we discuss how to relieve the computational burden of the Min-Max DeePC by reducing the dimension of prediction uncertainty and how to leverage disturbance feedback to reduce the conservativeness of robustification. We illustrate our results with high-fidelity, nonlinear, and noisy simulations of a four-area test system.

6. Data-Enabled Predictive Control for Quadcopters

   Ezzat Elokda, Jeremy Coulson, Paul N. Beuchat, John Lygeros, and Florian Dörfler

   International Journal of Robust and Nonlinear Control, 2021

   Abstract Link

   We study the application of a data-enabled predictive control (DeePC) algorithm for position control of real-world nano-quadcopters. The DeePC algorithm is a finite-horizon, optimal control method that uses input/output measurements from the system to predict future trajectories without the need for system identification or state estimation. The algorithm predicts future trajectories of the quadcopter by linearly combining previously measured trajectories (motion primitives). We illustrate the necessity of a regularized variant of the DeePC algorithm to handle the nonlinear nature of the real-world quadcopter dynamics with noisy measurements. Simulation-based analysis is used to gain insights into the effects of regularization, and experimental results validate that these insights carry over to the real-world quadcopter. Moreover, we demonstrate the reliability of the DeePC algorithm by collecting a new set of input/output measurements for every real-world experiment performed. The performance of the DeePC algorithm is compared to Model Predictive Control based on a first-principles model of the quadcopter. The results are demonstrated with a video of successful trajectory tracking of the real-world quadcopter.

7. On Average Controllability of Random Heat Equations with Arbitrarily Distributed Diffusivity

   Jeremy Coulson, Bahman Gharesifard, and Abdol-Reza Mansouri

   Automatica, 2019

   Abstract Link

   In this paper, we study the average controllability of a random heat equation, with the diffusivity serving as the random variable drawn from a general probability distribution. We show that the solutions of such random heat equations are both null and approximately controllable in average from an arbitrary open set of the domain and in an arbitrarily small time, recovering the known result when the random diffusivity is uniformly or exponentially distributed.

Conference Papers

1. Controller Implementability: A Data-Driven Approach

   Alberto Padoan, Jeremy Coulson, and Florian Dörfler

   2023 62nd IEEE Conference on Decision and Control (CDC), 2023

   Abstract Link arXiv

   We study the controller implementability problem, which seeks to determine if a controller can make the closed-loop behavior of a given plant match that of a desired reference behavior. We establish necessary and sufficient conditions for controller implementability which only rely on raw data. Subsequently, we consider the problem of constructing controllers directly from data. By leveraging the concept of canonical controller, we provide a formula to directly construct controllers that implement plant-compatible reference behaviors using measurements of both reference and plant behaviors.

2. A Quantitative and Constructive Proof of Willems’ Fundamental Lemma and Its Implications

   Julian Berberich, Andrea Iannelli, Alberto Padoan, Jeremy Coulson, Florian Dörfler, and Frank Allgöwer

   2023 American Control Conference (ACC), 2023

   Abstract Link

   Willems’ Fundamental Lemma provides a powerful data-driven parametrization of all trajectories of a controllable linear time-invariant system based on one trajectory with persistently exciting (PE) input. In this paper, we present a novel proof of this result which is inspired by the classical adaptive control literature and differs from existing proofs in multiple aspects. The proof involves a quantitative and directional PE notion, allowing to characterize robust PE properties via singular value bounds, as opposed to binary rank- based PE conditions. Further, the proof is constructive, i.e., we derive an explicit PE lower bound for the generated data. As a contribution of independent interest, we generalize existing PE results from the adaptive control literature and reveal a crucial role of the system’s zeros.

3. Behavioral Uncertainty Quantification for Data-Driven Control

   2022 IEEE 61st Conference on Decision and Control (CDC), 2022

   Abstract Link arXiv

   This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems’ fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.

4. Robust Adaptive Model Predictive Control of Quadrotors

   Alexandre Didier, Anilkumar Parsi, Jeremy Coulson, and Roy S. Smith

   2021 European Control Conference (ECC), 2021

   Abstract Link arXiv

   Robust adaptive model predictive control (RAMPC) is a novel control method that combines robustness guarantees with respect to unknown parameters and bounded disturbances into a model predictive control scheme. However, RAMPC has so far only been developed in theory. The goal of this paper is to apply RAMPC to a physical quadrotor experiment. To the best of our knowledge this is the first time that RAMPC has been applied in practice using a state space formulation. In doing so, we highlight important practical challenges such as computation of λ-contractive polytopes and dealing with measurement noise, and propose modifications to RAMPC so that it can be applied on a quadrotor. We first simulate quadrotor flight with a direct and a decoupled control architecture in different scenarios. The scenarios include: (i) an uncertain quadrotor mass and additive wind disturbance as part of a package delivery problem; and (ii) all rotor efficiencies drop as a power delivery problem. We then implement these scenarios on a physical quadrotor and present the experimental results.

5. Regularized and Distributionally Robust Data-Enabled Predictive Control

   Jeremy Coulson, John Lygeros, and Florian Dörfler

   2019 IEEE 58th Conference on Decision and Control (CDC), 2019

   Abstract Link arXiv

   In this paper, we study a data-enabled predictive control (DeePC) algorithm applied to unknown stochastic linear time-invariant systems. The algorithm uses noise-corrupted input/output data to predict future trajectories and compute optimal control policies. To robustify against uncertainties in the input/output data, the control policies are computed to minimize a worst-case expectation of a given objective function. Using techniques from distributionally robust stochastic optimization, we prove that for certain objective functions, the worst-case optimization problem coincides with a regularized version of the DeePC algorithm. These results support the previously observed advantages of the regularized algorithm. We illustrate the robustness of the regularized algorithm through a numerical case study.

6. Data-Enabled Predictive Control for Grid-Connected Power Converters

   Linbin Huang, Jeremy Coulson, John Lygeros, and Florian Dörfler

   2019 IEEE 58th Conference on Decision and Control (CDC), 2019

   Abstract Link

   We apply a novel data-enabled predictive control (DeePC) algorithm in grid-connected power converters to perform safe and optimal control. Rather than a model, the DeePC algorithm solely needs input/output data measured from the unknown system to predict future trajectories. We show that the DeePC can eliminate undesired oscillations in a grid-connected power converter and stabilize an unstable system. However, the DeePC algorithm may suffer from poor scalability when applied in high-order systems. To this end, we present a finite-horizon output-based model predictive control (MPC) for grid-connected power converters, which uses an N-step auto-regressive-moving-average (ARMA) model for system representation. The ARMA model is identified via an N-step prediction error method (PEM) in a recursive way. We investigate the connection between the DeePC and the concatenated PEM-MPC method, and then analytically and numerically compare their closed-loop performance. Moreover, the PEM-MPC is applied in a voltage source converter based HVDC station which is connected to a two-area power system so as to eliminate low-frequency oscillations. All of our results are illustrated with high-fidelity, nonlinear, and noisy simulations.

7. Data-Enabled Predictive Control: In the Shallows of the DeePC

   Jeremy Coulson, John Lygeros, and Florian Dörfler

   2019 18th European Control Conference (ECC), 2019

   Abstract Link arXiv

   We consider the problem of optimal trajectory tracking for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioural systems theory approach to learn a non-parametric system model used to predict future trajectories. The DeePC algorithm is shown to be equivalent to the classical and widely adopted Model Predictive Control (MPC) algorithm in the case of deterministic linear time-invariant systems. In the case of nonlinear stochastic systems, we propose regularizations to the DeePC algorithm. Simulations are provided to illustrate performance and compare the algorithm with other methods.

8. On the Termination Time of the One-Sided Asymmetric Hegselmann-Krause Dynamics

   Jeremy Coulson, Drew Steeves, Bahman Gharesifard, and Behrouz Touri

   2015 American Control Conference (ACC), 2015

   Abstract Link

   In this paper, we provide a novel upper bound for the termination time of the one-dimensional asymmetric Hegselmann-Krause dynamics, when the asymmetry is one-sided. In addition to the number of agents, our upper bound depends on the ratio of asymmetry and the confidence range in the opinions of agents, and recovers the known O(n3) results of the symmetric case. Our proof technique relies on a novel Lyapunov-like function, which measures the spread of the opinion profile. As a by-product, we fully characterize the switching pattern in the opinions of the agents.

Extended Abstracts

1. Geometrically Robust Least Squares through Manifold Optimization

   Jeremy Coulson, Alberto Padoan, and Cyrus S Mostajerin

   Extended Abstract in International Symposium on Mathematical Theory of Networks and Systems, 2024

   arXiv
2. Mind the Gap: The Role of Metrics in Data-Driven Modelling

   Alberto Padoan and Jeremy Coulson

   Extended Abstract in Symposium on System Identification, 2024
3. Robust Fundamental Lemma for Data-Driven Control

   Extended Abstract in International Symposium on Mathematical Theory of Networks and Systems, 2022

   arXiv
4. Hands-on Quadcopter Education at All Levels

   Paul N Beuchat, Jeremy Coulson, and John Lygeros

   Extended Abstract in International Federation of Automatic Control (IFAC) World Congress, 2020

Theses

1. Data-Enabled Predictive Control: Theory and Practice

   Jeremy Coulson

   2022
2. Average Controllability of Random Heat Equations

   Jeremy Coulson

   2017
3. Synchronization of Coupled Oscillators in Power Networks

   Jeremy Coulson

   2015

Miscellaneous

1. Jeremy Coulson [PhDs in Control]

   Jeremy Coulson

   IEEE Control Systems Magazine, 2023

   Abstract Link

   Q. How would you pitch your Ph.D. dissertation in one paragraph?