publications

2026

1. L-CSS+CDC

   Control of the state transition matrix via factorization into positive definite factors

   M. Abdelgalil and T. T. Georgiou

   IEEE Control Systems Letters, 2026

   Abs DOI

   The factorization of an arbitrary matrix Φ with positive determinant into a product of positive-definite ones provides a piece-wise smooth time-varying control protocol to realize Φ as the state transition matrix of a linear system via state feedback. The factors, being symmetric and positive-definite, realize a succession of gradient flows ensuring the avoidance of shocks. We relate such a factorization to a composition of optimal transport maps between suitably constructed Gaussian distributions. Our analysis provides a principled construction of such factorizations that, in addition, allows a handle on the condition number of the factors which relates to control effort.

2. L-CSS+CDC

   A separation principle for stochastic feedback optimization

   M. Tang, M. Abdelgalil, and J. I. Poveda

   IEEE Control Systems Letters, 2026

   Abs DOI

   We study the problem of online feedback optimization for stochastic linear plants and quadratic performance costs in the presence of an unknown disturbance and persistent white noise. For this problem, we introduce a novel two-timescale control architecture consisting of a static feedback term and a dynamically tuned feedforward term. Through singular perturbation analysis, we show that the steady-state mean of the system converges to the feasible optimizer of the problem, independently of the feedback term, and the steady-state covariance converges to the standard LQR baseline up to a small bias of order 𝒪(ε), where ε is the learning rate of the optimization dynamics. In this sense, our results highlight a novel separation principle that justifies a sequential design approach for stochastic feedback optimization: the feedback term may be designed offline via LQR techniques to minimize the covariance penalty, e.g., using a Riccati equation, while the dynamic feedforward leverages a gradient-based architecture that rejects the unknown disturbance from the steady-state mean, all while incurring only an 𝒪(ε)-optimality gap. Numerical simulations are provided to validate the theory.

3. L-CSS+CDC

   On the isospectral nature of minimum-shear covariance control

   R. Sabbagh, A. Eldesoukey, M. Abdelgalil, and 1 more author

   IEEE Control Systems Letters, 2026

   Abs DOI arXiv

   We revisit Brockett’s attention in the context of bilinear gradient flow of an ensemble, and explore an alternative formalism that aims to reduce shear by minimizing the conditioning number of the dynamics; equivalently, we minimize the range of the eigenvalues of the dynamics. Remarkably, the evolution is isospectral, and this property is inherited by the coupled nonlinear dynamics of the control problem from a Lax isospectral flow.

4. L-CSS+CDC

   On the strong stability of an edge-assisted max-weight policy with observation and control-input delays

   X. Zhang, A. Bura, M. Abdelgalil, and 2 more authors

   IEEE Control Systems Letters, 2026

   Abs DOI

   We study the strong stability of Max-Weight scheduling in wireless queueing systems with both observation and control-input delays. In these systems, channel state information reaches an edge controller only after measurement and reporting latency, while the selected schedule is implemented after an additional actuation delay, creating a decision–execution mismatch. Although prior work has studied delayed state information and scheduling delays separately, a unified stability analysis under simultaneous observation and control-input delays remains lacking. We develop a Lyapunov–Foster framework for the resulting stochastic delayed difference inclusion. The main result gives an explicit sufficient condition for strong stability and a closed-form bound on the time-average backlog. The condition separates delayed-observation and delayed-execution effects through two penalty terms, clarifying how each delay mechanism reduces the available stability margin. Numerical experiments connect the sufficient condition to empirical behavior and indicate that, in the tested regimes, control-input delay has a stronger impact on backlog growth than observation delay.

5. Automatica

   Hybrid minimum-seeking in synergistic Lyapunov functions: Robust global stabilization under unknown control directions

   M. Abdelgalil and J. I. Poveda

   Automatica, 2026

   Abs DOI arXiv

   We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions and the presence of topological obstructions that prevent the existence of smooth global control Lyapunov functions. Building on a recently developed Lie-bracket averaging result for hybrid dynamic inclusions presented in, we propose a novel class of universal hybrid feedback laws that achieve robust global practical stability by identifying the minimum point of a set of appropriately chosen synergistic Lyapunov functions. As concrete applications of our results, we synthesize different hybrid high-frequency high-amplitude feedback laws for the solution of robust global stabilization problems on various types of manifolds under unknown control directions, as well as controllers for obstacle avoidance problems in vehicles characterized by kinematic models describing both holonomic and non-holonomic models. By leveraging Lie-bracket averaging for hybrid systems, we also show how the proposed hybrid minimum-seeking feedback laws can overcome lack of controllability during persistent (bounded) periods of time. Numerical simulation results are presented to illustrate the main results.

6. Automatica

   Persistently resetting integrators for gradient learning: A framework for model-free feedback optimization

   M. Abdelgalil and J. I. Poveda

   Automatica, 2026

   Abs DOI

   We study a novel class of algorithms for solving model-free feedback optimization problems based on persistent resetting integrators for gradient learning (PRINGL), which are integrators that are reset at the same frequency at which the plant is dithered. It is shown that PRINGLs serve as core mechanisms for real-time gradient estimation when only cost function measurements are available. Unlike existing approaches such as averaging, PRINGLs can produce global real-time gradient estimates with uniformly bounded perturbations of arbitrarily small magnitude. In this sense, PRINGLs serve as robust hybrid “oracles” suitable for interconnection with discrete-time optimization algorithms in closed-loop operation. It is proven that PRINGLs yield global stability properties for a broad class of cost functions, surpassing the local or semi-global guarantees offered by classical approaches. The proposed framework naturally bridges physical systems, modeled as continuous-time plants where continuous exploration is essential, with digital algorithms, represented as discrete-time optimization methods. This integration of physical and digital components allows for the application of a broad range of well-established optimization techniques, each offering unique performance benefits suited to different applications—such as accelerated convergence through momentum, safety assurances via projections, etc. Closed-loop stability guarantees are established using unifying tools from hybrid systems theory. The main results are illustrated using different numerical examples.

7. NAHS

   Omega-limit sets and input-to-state stability in power grids with switching equilibria

   M. Abdelgalil, V. Shenoy, G. Cavraro, and 2 more authors

   Nonlinear Analysis: Hybrid Systems, 2026

   DOI
8. TAC

   The holonomy of optimal mass transport: The Gaussian-linear case

   M. Abdelgalil and T. T. Georgiou

   IEEE Transactions on Automatic Control, 2026

   Abs DOI arXiv

   The theory of Monge-Kantorovich Optimal Mass Transport (OMT) has in recent years spurred a fast developing phase of research in stochastic control, control of ensemble systems, thermodynamics, data science, and several other fields in engineering and science. We herein introduce a new type of transportation problems. The salient feature of these problems is that particles/agents in the ensemble are labeled and their relative position along their journey is of interest. Of particular importance in our program are control laws that steer ensembles along cycles ensuring that individual particles return to their original position. This feature is in contrast with the classical theory of optimal transport where the primary object of study is the path of probability densities, without any concern about particle labels. In the theory that we present, we focus on the case Gaussian distributions and linear dynamics, and explore a hitherto unstudied sub-Riemannian structure of Monge-Kantorovich transport where the relative position of particles along their journey is modeled by the holonomy of the transportation schedule. From this vantage point, we discuss several other problems of independent interest.

2025

1. L-CSS+ACC

   On the instability of Nesterov’s ODE under non-conservative vector fields

   D. E. Ochoa, M. Abdelgalil, and J. I. Poveda

   IEEE Control Systems Letters, 2025

   Abs DOI arXiv

   We study the instability properties of Nesterov’s ODE in non-conservative settings, where the driving term is not necessarily the gradient of a potential function. While convergence properties under Nesterov’s ODE are well-characterized for optimization settings with gradient-based driving terms, we show that the presence of arbitrarily small non-conservative terms can lead to instability, a phenomenon previously observed empirically via numerical studies in optimization and game-theoretic problems. Our instability analysis combines multi-time scale techniques, such as averaging via variations-of-constants formula, and Floquet Theory, focusing on systems where the vector field is linear and its Helmholtz decomposition reveals a non-vanishing non-conservative component. To resolve the instability issue, the dynamics under non-vanishing non-conservative components, we study a regularization mechanism based on restarting. The resulting system is a hybrid dynamical system that mirrors Nesterov’s ODE during intervals of flow, and implements resets of the momentum state through discrete periodic jumps. For this hybrid system, we establish novel explicit bounds on the resetting period that ensure the decrease of a suitable Lyapunov function, guaranteeing not only stability but also "accelerated" convergence rates under suitable smoothness and strong monotonicity properties on the driving term. Numerical simulations support our theoretical results.

2. TAC

   Collective steering in finite time: Controllability on GL⁺(n, ℝ)

   M. Abdelgalil and T. T. Georgiou

   IEEE Transactions on Automatic Control, 2025

   Abs DOI

   We consider the problem of steering a collection ofnparticles that obey identicaln-dimensional linear dynamics via a common state feedback law towards a rearrangement of their positions, cast as a controllability problem for a dynamical system evolving on the space of matrices with positive determinant. We show that such a task is always feasible and, moreover, that it can be achieved arbitrarily fast. We also show that an optimal feedback control policy to achieve a similar feat, may not exist. Furthermore, we show that there is no universal formula for a linear feedback control law to achieve a rearrangement, optimal or not, that is everywhere continuous with respect to the specifications. We conclude with partial results on the broader question of controllability of dynamics on orientation-preserving diffeomorphisms.

3. TAC

   On Lie-bracket averaging for hybrid dynamical systems with applications to model-free control and optimization

   M. Abdelgalil and J. I. Poveda

   IEEE Transactions on Automatic Control, 2025

   Abs DOI

   The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine continuous and discrete dynamics. However, most averaging results for hybrid systems are limited to first-order methods, hindering their use in systems and algorithms that require high-order averaging techniques, such as hybrid Lie-bracket-based extremum seeking algorithms and hybrid vibrational controllers. To address this limitation, we introduce a novel high-order averaging theorem for analyzing the stability of hybrid dynamical systems with high-frequency periodic flow maps. These systems incorporate set-valued flow maps and jump maps, effectively modeling well-posed differential and difference inclusions. By imposing appropriate regularity conditions, we establish results on(T, ε)-closeness of solutions and semi-global practical asymptotic stability for sets. These theoretical results are then applied to the study of three distinct applications in the context of hybrid model-free control and optimization via Lie-bracket averaging.

4. NeurIPS WS

   Stochastic Lie bracket approximations for zeroth-order optimization on manifolds

   M. Abdelgalil and J. I. Poveda

   In Dynamics at the Frontiers of Optimization, Sampling, and Games Workshop, Conference on Neural Information Processing Systems (NeurIPS), 2025

   HTML
5. CDC

   On event-triggered extremum seeking via standard and Lie-bracket averaging: A hybrid dynamical systems approach

   M. Abdelgalil and J. I. Poveda

   In Proc. IEEE Conference on Decision and Control, 2025

   Abs DOI arXiv

   We introduce and analyze the stability of a class of event-triggered extremum-seeking algorithms designed to solve resource-aware, model-free, optimization problems. Leveraging recent advances in Lie-Bracket Averaging for hybrid systems, we demonstrate that the proposed controllers can be formulated as well-posed multi-time-scale hybrid systems that satisfy key regularity, stability, and robustness properties. In extremum-seeking systems, exploration and exploitation are inherently coupled. This coupling necessitates careful consideration in the design of the event-triggered controller. To address this challenge, we incorporate a low-pass filter into the algorithm and carefully design the flow and jump sets of the resulting hybrid system. The resulting controller renders the optimal point semi-globally practically asymptotically stable with solutions exhibiting a uniform semi-global dwell time. We also demonstrate how the proposed event-triggered scheme can be modified to allow analysis using traditional averaging tools for hybrid systems by introducing two independent tunable parameters in the controller. Numerical simulations are presented to validate and illustrate the theoretical results.

6. CDC

   Control of the state transition via state feedback

   M. Abdelgalil and T. T. Georgiou

   In Proc. IEEE Conference on Decision and Control, 2025

   Abs DOI

   We study a nonlinear control problem in which linear dynamics are regulated by a time-varying state-feedback law. The nonlinearity arises from the bilinear interaction between the feedback gain and the state. We show that the classical Kalman controllability condition, easily seen to be necessary, is also sufficient in this setting. More strongly, we establish that one can not only prescribe the terminal state vector over any finite horizon, but also steer the entire state-transition matrix to an arbitrary target with positive determinant.Our interest in controlling the state-transition matrix is motivated by the problem of regulating ensembles of agents that evolve according to the given dynamics, where a common time-varying feedback gain is broadcast and applied by all agents. We show that, under a suitable protocol, a collection of particles can be repositioned arbitrarily fast into any admissible terminal configuration.While this work was initially intended as an extended abstract for the journal article [1], which develops broader results on controllability over diffeomorphism groups, the present article now provides an independent constructive derivation of main result and of the feedback protocols that achieve prescribed terminal state-transition matrices.

7. CDC

   Collective steering: Tracer-informed dynamics

   A. Eldesoukey, M. Abdelgalil, and T. T. Georgiou

   In Proc. IEEE Conference on Decision and Control, 2025

   Abs DOI arXiv

   We consider control and inference problems where control protocols and internal dynamics are informed by two types of constraints. Our data consist of i) statistics on the ensemble and ii) trajectories or final disposition of selected tracer particles embedded in the flow. Our aim is i’) to specify a control protocol to realize a flow that meets such constraints or ii’) to recover the internal dynamics that are consistent with such a data set. We analyze these problems in the setting of linear flows and Gaussian distributions. The control cost is taken to be a suitable action integral constrained by either the trajectories of tracer particles or their terminal placements.

2024

1. SCL

   Initialization-free Lie-bracket extremum seeking

   M. Abdelgalil and J. I. Poveda

   Systems & Control Letters, 2024

   Abs DOI arXiv

   Stability results for extremum seeking control in ℝⁿ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets of initial conditions often demands a stringent global Lipschitz condition on the cost function, which is rarely satisfied by practical applications. In this paper, we address this challenge by leveraging tools from higher-order averaging theory. In particular, we establish a novel second-order averaging result with global (practical) stability implications. By leveraging this result, we characterize sufficient conditions on cost functions under which uniform global practical asymptotic stability can be established for a class of extremum-seeking systems acting on static maps. Our sufficient conditions include the case when the gradient of the cost function, rather than the cost function itself, satisfies a global Lipschitz condition, which covers quadratic cost functions. Our results are also applicable to vector fields that are not necessarily Lipschitz continuous at the origin, opening the door to non-smooth Lie-bracket ES dynamics. We illustrate all our results via different analytical and/or numerical examples.

2023

1. ARC

   Multi-time scale control and optimization via averaging and singular perturbation theory: From ODEs to hybrid dynamical systems

   M. Abdelgalil, D. E. Ochoa, and J. I. Poveda

   Annual Reviews in Control, 2023

   Abs DOI

   Multi-time scale techniques based on singular perturbations and averaging theory are among the most powerful tools developed for the synthesis and analysis of feedback control algorithms. This paper introduces some of the recent advances in singular perturbation theory and averaging theory for continuous-time dynamical systems modeled as ordinary differential equations (ODEs), as well as for hybrid dynamical systems that combine continuous-time dynamics and discrete-time dynamics. Novel multi-time scale analytical tools based on higher-order averaging and singular perturbation theory are also discussed and illustrated via different examples. In the context of hybrid dynamical systems, a class of sufficient Lyapunov-based conditions for global stability results are also presented. The analytical tools are illustrated through various new architectures and algorithms within the context of adaptive and extremum-seeking systems. These tools are suitable for the study of model-free optimization and stabilization problems that require the synergistic use of continuous-time and discrete-time feedback. The paper aims to acquaint the reader with a range of modern tools for studying multi-time scale phenomena in optimization and control systems, providing some guidelines for future research in this field.

2. ACC

   Singularly perturbed averaging with application to bio-inspired 3D source seeking

   M. Abdelgalil, A. Eldesoukey, and H. Taha

   In Proc. American Control Conference, 2023

   Best Student Paper Award Abs DOI arXiv

   Best Student Paper Award, 2023 American Control Conference.

   We analyze a class of singularly perturbed high-amplitude, high-frequency oscillatory systems that arises in extremum seeking applications. We provide explicit formulas for averaging and establish the convergence of the trajectories of this class of systems to the trajectories of a suitably averaged reduced order system by combining the higher order averaging theorem with singular perturbation techniques. Finally, we propose a novel bio-inspired 3D source seeking algorithm and establish its singular practical stability.

3. SciTech

   Feedback oscillatory control of roll instability during stall using the LIBRA mechanism

   M. Abdelgalil and H. Taha

   In Proc. AIAA SciTech Forum, 2023

   Abs DOI

   The goal of this paper is to design a stabilizing feedback controller of roll instability near stall. This problem becomes immensely challenging since the aileron sensitivity is vanishes and even reversed sign at stall. This challenge is overcome by employing the recently developed Lie Bracket Roll Augmentation (LIBRA) mechanism. In this mechanism,the nonlinear dynamics of the airplane near stall is exploited to achieve a rolling motion that is independent of the aileron sensitivity. Rather, it depends on the variation of the aileron sensitivity with the angle of attack which is non-zero at stall. The open loop characteristics of the LIBRA mechanism have been studied previously. The contribution of the current manuscript lies in using the LIBRA mechanism in a feedback fashion to stabilize the roll unstable dynamics near stall using a stabilization scheme based on motion planning techniques for highly oscillatory inputs.

2022

1. PRE

   Sea urchin sperm exploit extremum seeking control to find the egg

   M. Abdelgalil, Y. Aboelkassem, and H. Taha

   Physical Review E, 2022

   Abs DOI arXiv

   Sperm cells perform extremely demanding tasks with minimal capabilities. The cells must quickly navigate in a noisy environment to find an egg within a short time window for successful fertilization without any global positioning information. Many research efforts have been dedicated to deriving mathematical principles that explain their superb navigation strategy. Here we show that the navigation strategy of sea urchin sperm, also known as helical klinotaxis, is a natural implementation of a well-established adaptive control paradigm known as extremum seeking. This bridge between control theory and the biology of taxis in microorganisms is expected to deepen our understanding of the process. For example, the formulation leads to a coarse-grained model of the signaling pathway that offers new insights on the peculiar switching-like behavior between high and low gain steering modes observed in sea urchin sperm. Moreover, it may guide engineers in developing bio-inspired miniaturized robots with minimal sensors.

2. L-CSS+CDC

   Recursive averaging with application to bio-inspired 3D source seeking

   M. Abdelgalil and H. Taha

   IEEE Control Systems Letters, 2022

   Also presented at the 2022 IEEE Conference on Decision and Control.

   Abs DOI arXiv

   We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the averaging theorem. Moreover, we introduce a novel bio-inspired 3D source seeking algorithm for rigid bodies with a collocated sensor and prove its practical stability under typical assumptions on the source signal strength field by combining our averaging results with singular perturbation.

3. SciTech

   Observations on the use of gap metric in model reduction

   A. Eldesoukey, M. Abdelgalil, and H. Taha

   In Proc. AIAA SciTech Forum, 2022

   Abs DOI

   We review the use of the gap metric to synthesize a reduced-order plant whose closed-loop behavior is similar to that of an original (typically higher-order) plant. That is, our aim is to look into the use of the gap metric as a cost function for optimal estimation of a reduced model parameters such that a control law, designed based on the reduced-order model, would result in a satisfactory closed-loop response of the original. To this end, the minimization of the gap metric is reviewed with different cases of LTI and nonlinear systems. Moreover, the use of the data-driven gap distance as a cost function is examined; by employing the data-driven gap metric, we explore the possibility of obtaining a reduced-order model only from a single input-output trajectory of the original plant. Constructive examples are given with following practical observations on the validity and effectiveness of each model reduction method.

2021

1. Automatica

   Lie bracket approximation-based extremum seeking with vanishing input oscillations

   M. Abdelgalil and H. Taha

   Automatica, 2021

   Abs DOI arXiv

   In recent years, an approach to extremum seeking control made it possible to design control vector fields that lead to asymptotic stability of the minimum point provided that the minimum value of the function is known a priori. In this work, we aim to relax that assumption. We propose an extremum-seeking control law that converges to the minimum point with vanishing control oscillations, without access to the minimum value of the cost function. We provide a numerical example to support our results.

2. SciTech

   On the motion planning and feedback stabilization of nonlinear systems with drift

   M. Abdelgalil, A. Hassan, and H. Taha

   In Proc. AIAA SciTech Forum, 2021

   Abs DOI

   The motion planning problem (MPP) is the problem of finding a control input that steers a control system between two arbitrarily given points. Several algorithms have been developed for the motion planning of nonlinear driftless systems over the 1990’s using differential geometric control tools. However, little is known about MPP of nonlinear systems with drift. With the contemporary research flurry on motion planning in the robotics community, mostly using optimal control and machine learning techniques, we aim in this paper to demonstrate the capabilities of differential geometric control theory in solving the MPP for nonlinear systems with drift and also in designing feedback stabilization using Lie brackets for systems that fail Brockett’s necessary condition for stabilization using smooth feedback.