Article Dans Une Revue IMA Journal of Mathematical Control and Information Année : 2025

Underactuated boundary control of a linearized Saint-Venant equation

Résumé

This paper deals with the stabilization of one-dimensional linearized, shock-free Saint-Venant equations, which are widely used in fluid modeling. The approach focuses on four under-actuated hyperbolic partial differential equations, combining Volterra transformations inspired by backstepping techniques. The system is reduced to an integral difference equation, allowing for stability analysis the use of spectral methods. A distributed state feedback controller is designed to eliminate integral terms by solving a Fredholm equation. This result effectively addresses challenges related to under-actuation and lays the foundation for extending stabilization techniques to nonlinear scenarios.

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Dates et versions

hal-05033220 , version 1 (14-04-2025)

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Jean Auriol, Adam Braun, Mohand Ouidir Amirat, Mathieu Bajodek. Underactuated boundary control of a linearized Saint-Venant equation. IMA Journal of Mathematical Control and Information, 2025, ⟨10.1093/imamci/dnnxxx⟩. ⟨hal-05033220⟩
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