Mahmoud Abdelgalil

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• Doctor of Philosophy
• Postdoctoral Researcher at University of California, San Diego

We consider the problem of robust global stabilization for a control-affine systems with dynamic uncertainty in the control directions and in the presence of topological obstructions that preclude the existence of smooth global control Lyapunov functions. By leveraging a recent Lie-bracket averaging result for hybrid dynamic inclusions introduced i...

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. Specifically, OMT endowed the space of probability distributions with a rich Riemannian-li...

We consider the problem of steering a collection of n particles that obey identical n-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 feasibl...

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 meth...

We study a novel class of algorithms for solving model-free feedback optimization problems in dynamical systems. The key novelty is the introduction of \emph{persistent resetting learning integrators} (PRLI), which are integrators that are reset at the same frequency at which the plant is dithered using exploratory signals for model-free optimizati...

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-c...

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Stability results for extremum seeking control in R^n 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 satisfi...

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 d...

Dynamical systems characterized by oscillatory behaviors and well-defined average vector fields have traditionally been subjects of stability analysis through methodologies rooted in averaging theory. Such tools have also found application in the stability analysis of systems that combine continuous-time dynamics and discrete-time dynamics, referre...

We propose a novel 3D source seeking algorithm for rigid bodies with a non-collocated sensor inspired by the chemotactic navigation strategy of sea urchin sperm known as helical klinotaxis. We work directly with the rotation group SO(3) without parameterization in representing the attitude of a rigid body. As a consequence, the proposed algorithm d...

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 derive mathematical principles that explain their superb navig...

We analyze a class of high-frequency, high-amplitude 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 higher-order averaging. Moreover, we introduce a novel bio-inspired 3D source seeking algorithm for rigid bodies equi...

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 poi...

In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We demonstrate the effectiveness of the simulator and its accuracy in long term integration of mechanical systems without...