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math.OC2026

Nonsmooth High-Order Averaging Theory with Application to Extremum Seeking Optimization and Control

Hesham Abdelfattah, Sameh A. Eisa, Peter Stechlinski

In this paper, we introduce a higher-order averaging theory and method for a wide range of nonsmooth systems that are generally characterized by the classical averaging canonical f…

math.OC2026

Extremum seeking with exponential convergence via high-order Lie bracket approximations

Victoria Grushkovskaya, Sameh A. Eisa

This paper focuses on the further development of the Lie bracket approximation approach for optimization and control via extremum seeking systems. Classical results in this area pr…

math.OC2026

Model-Free Optimization and Control of Rigid Body Dynamics: An Extremum Seeking for Vibrational Stabilization Approach

Rohan Palanikumar, Ahmed A. Elgohary, Simone Martini +1

In this paper, we introduce a model-free, real-time, dynamic optimization and control method for a class of rigid body dynamics. Our method is based on a recent extremum seeking co…

math.OC2026

Model-free source seeking of exponentially convergent unicycle: theoretical and robotic experimental results

Rohan Palanikumar, Ahmed A. Elgohary, Victoria Grushkovskaya +1

This paper introduces a novel model-free, real-time unicycle-based source seeking design. This design autonomously steers the unicycle dynamic system towards the extremum point of…

math.OC2025

Hovering Flight in Flapping Insects and Hummingbirds: A Natural Real-Time and Stable Extremum Seeking Feedback System

Ahmed A. Elgohary, Sameh A. Eisa

In this paper, we take an initial and novel step toward characterizing the physics of the hovering phenomenon in flapping insects and hummingbirds as a new class of extremum seekin…

math.OC2025

Extremum Seeking for Controlled Vibrational Stabilization of Second Order Mechanical Systems

Ahmed A. Elgohary, Sameh A. Eisa

This paper presents a novel extremum seeking control (ESC) approach for the vibrational stabilization of a class of mechanical systems (e.g., systems characterized by equations of…