The content discusses the generalization of Sontag's formula to systems not affine in control, focusing on PDEs with boundary actuation. It introduces a continuous universal controller for systems with depressed cubic, quadratic, or depressed quartic dependence on the control. The article proves the results in the context of convection-reaction-diffusion PDEs with Dirichlet actuation. It extends Sontag's formula to non-affine systems and presents a new Lyapunov approach for boundary control of nonlinear PDEs. The content is structured into sections discussing the introduction and main result, going beyond control-affine systems, the motivation, the main result, construction of universal controllers, a numerical example, and a conclusion. The article also references related works and provides insights into the stabilization of challenging PDE systems.
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by Mohamed Cami... at arxiv.org 03-28-2024
https://arxiv.org/pdf/2403.18071.pdfDeeper Inquiries