{"ID":2841173,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11994","arxiv_id":"2511.11994","title":"Extremum-Seeking Boundary Control for Schrödinger-Type PDEs","abstract":"This paper addresses the design and analysis of an extremum-seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by complex-valued partial differential equations (PDEs) of Schrodinger type. The system is actuated at one boundary, and the map input is defined as a real-valued quadratic functional corresponding to the squared norm of the complex state at the uncontrolled boundary. An isomorphism between the complex Hilbert space and its two-dimensional real-valued representation is established to enable the use of the standard multivariable Newton-based ES method. To compensate for the PDE actuation dynamics, a boundary control strategy based on a two-step backstepping procedure is employed. With a perturbation-based estimate of the Hessian inverse, the local exponential stability to a small neighborhood of the unknown extremum point is proved. A numerical example illustrates the effectiveness of the proposed extremum-seeking methodology.","short_abstract":"This paper addresses the design and analysis of an extremum-seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by complex-valued partial differential equations (PDEs) of Schrodinger type. The system is actuated at one boundary, and the map input is defined as a real-...","url_abs":"https://arxiv.org/abs/2511.11994","url_pdf":"https://arxiv.org/pdf/2511.11994v1","authors":"[\"Paulo Henrique Foganholo Biazetto\",\"Gustavo Artur de Andrade\",\"Tiago Roux Oliveira\",\"Miroslav Krstic\"]","published":"2025-11-15T02:16:23Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}