{"ID":2822759,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.02607","arxiv_id":"2601.02607","title":"Extremum Seeking Control for Wave-PDE Actuation with Distributed Effects","abstract":"This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of infinite-dimensional systems, we first solve the trajectory generation problem to re-design the additive perturbation signal of the ESC system. Then, we develop a boundary control law through the backstepping method to compensate for the wave PDE with distributed effects, which ensures the exponential stability of the average closed-loop system by means of a Lyapunov-based analysis. At last, by employing the averaging theory for infinite-dimensional systems, we prove that the closed-loop trajectories converge to a small neighborhood surrounding the optimal point. Numerical simulations are presented to illustrate the effectiveness of the proposed method.","short_abstract":"This paper deals with the gradient-based extremum seeking control (ESC) with actuation dynamics governed by distributed wave partial differential equations (PDEs). To achieve the control objective of real-time optimization for this class of infinite-dimensional systems, we first solve the trajectory generation problem...","url_abs":"https://arxiv.org/abs/2601.02607","url_pdf":"https://arxiv.org/pdf/2601.02607v1","authors":"[\"Elisio Juvenal Muchave\",\"Pedro Henrique Silva Coutinho\",\"Tiago Roux Oliveira\",\"Miroslav Krstić\"]","published":"2026-01-05T23:52:04Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}