2021/05/09 by Sameer Pokhrel, Pokhrel, Sameer, Sameh A. Eisa +1 · 1 citation
Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #Extremum Seeking Control Systems #FOS: Mathematics #Laser-Matter Interactions and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2105.03985
openalex publication_date 2021/05/09 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Control-affine Extremum Seeking Control (ESC) systems have been increasingly studied and applied in the last decade. In a recent effort, many control-affine ESC structures have been generalized in a unifying class and their stability was analyzed. However, guaranteeing vanishing oscillations at the extremum point for said class requires strong conditions that may not be feasible or easy to check/design by the user, especially when the gradient of the objective function is unknown. In this paper, we introduce a control-affine ESC structure that remedies this problem such that: (i) its oscillations attenuate structurally via a novel application of a geometric-based Kalman filter and a Lie bracket estimation approach; and (ii) its stability is characterized by a time-dependent (one-bound) condition that is easier to check and relaxed when compared to the generalized approach mentioned earlier. We provide numerical simulations of three problems to demonstrate the effectiveness of our proposed ESC; these problems cannot be solved with vanishing oscillations using the generalized approach in the literature.