{"ID":5937723,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-08T15:36:38.046107012Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04361","arxiv_id":"2607.04361","title":"Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part I: Volterra Truncation","abstract":"Backstepping for nonlinear PDEs yields exact feedback linearizing laws in the form of infinite Volterra series -- elegant in theory, but with challenges for implementation. This paper shows that even very low-order truncations of such controllers, no longer exactly linearizing, retain the stabilizing power. The key insight is that higher-order terms become negligible near the origin, so stability is recovered for any fixed truncation order by restricting the initial condition size. We establish spatial sup-norm results: finite-time practical stability and asymptotic stability characterized by a class-$\\mathcal{KL}$ estimate. The region-of-attraction estimate grows with the truncation order and shrinks with the growth rate of the nonlinearity. The analysis overcomes the lack of pointwise kernel bounds and resolves well-posedness of the nonlinear closed loop, showing that surprisingly simple approximations already capture the essence of nonlinear PDE feedback linearization.","short_abstract":"Backstepping for nonlinear PDEs yields exact feedback linearizing laws in the form of infinite Volterra series -- elegant in theory, but with challenges for implementation. This paper shows that even very low-order truncations of such controllers, no longer exactly linearizing, retain the stabilizing power. The key ins...","url_abs":"https://arxiv.org/abs/2607.04361","url_pdf":"https://arxiv.org/pdf/2607.04361v1","authors":"[\"Miroslav Krstic\"]","published":"2026-07-05T15:38:35Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}