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arXiv · 2607.04361

Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part I: Volterra Truncation

Miroslav Krstic
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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.

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Miroslav Krstic. 2026-07-05. Approximate Feedback Linearization for a Nonlinear Hyperbolic PDE Class -- Part I: Volterra Truncation. https://arxiv.org/abs/2607.04361

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