Extremum Seeking for Controlled Vibrational Stabilization of Second Order Mechanical Systems

Abstract: 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 motion resulting from Newton second law or Euler-Lagrange mechanics). Inspired by flapping insects mechanics, the proposed ESC approach is operable by only one perturbation signal and can admit generalized forces that are quadratic in velocities. We test our ESC, and compare it against approaches from literature, on some classical mechanical systems (e.g., mass-spring and an inverted pendulum systems). We also provide a novel, first-of-its-kind, application of the introduced ESC by achieving a 1D model-free source-seeking of a flapping system.