2022/03/31 by Mahmoud Abdelgalil, Abdelgalil, Mahmoud, Asmaa Eldesoukey +3 · 1 citation
Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #Dynamical Systems (math.DS) #Extremum Seeking Control Systems #FOS: Mathematics #Mechanical and Optical Resonators #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2203.16808
openalex publication_date 2022/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.