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arXiv · 2511.11994

Extremum-Seeking Boundary Control for Schr\"odinger-Type PDEs

Paulo Henrique Foganholo Biazetto·Gustavo Artur de Andrade·Tiago Roux Oliveira·Miroslav Krstic
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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.

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Paulo Henrique Foganholo Biazetto, Gustavo Artur de Andrade, Tiago Roux Oliveira, Miroslav Krstic. 2025-11-15. Extremum-Seeking Boundary Control for Schr\"odinger-Type PDEs. https://arxiv.org/abs/2511.11994

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