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Backstepping Control of First-Order Hyperbolic Equations in Arbitrary Dimensions with Non-Trapping Characteristics
Mohamed Cami · 2026-05-26 · via math updates on arXiv.org

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Abstract:This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by the characteristic flow of the time-invariant transport operator, transforming the original multidimensional system into a continuum of decoupled one-dimensional hyperbolic equations evolving along individual characteristic curves. A backstepping controller is then designed for each equation in the decomposition, and the resulting control laws are reassembled in the original coordinates to achieve finite-time stabilization of the full system. The framework relies on the existence of characteristic curves foliating the spatial domain, with uniformly bounded transit times (non-trapping).
Subjects: Systems and Control (eess.SY); Analysis of PDEs (math.AP)
Cite as: arXiv:2605.25217 [eess.SY]
  (or arXiv:2605.25217v1 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2605.25217

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Mohamed Camil Belhadjoudja [view email]
[v1] Sun, 24 May 2026 18:51:39 UTC (241 KB)