2023 Academic Thesis Prize: Nicolas VANSPRANGHE

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Nicolas VANSPRANGHE received the 2023 Academic Thesis Prize for his research work among PhDs graduating in 2022.

Thesis Title - Contributions to infinite-dimensional nonlinear control theory.

Nicolas VANSPRANGHE - Prix de thèse académique 2023This thesis concerns the problems of feedback stabilization and output regulation for infinite- dimensional nonlinear systems. First, we study the stability of a one-dimensional wave equation with a nonlinear velocity feedback at one extremity of the domain and a nonlinear dynamic boundary condition at the other end. This model is inspired by the behavior of torsional vibrations along drill strings, and the boundary dynamics represent a nonlinear anti-damping at the rock-bit interface that renders the uncontrolled plant unstable. Exponential stability of the set of stationary solutions is investigated by Lyapunov methods. In a second part, we consider the multi-dimensional wave equation supplied with a nonlinear and nonlocal Dirichlet feedback control acting on a part of the boundary. Well-posedness and asymptotic stability of the closed-loop dynamics are established using nonlinear contraction semigroup arguments combined with the LaSalle invariance principle and unique continuation for waves. When the feedback nonlinearity has linear growth around zero (e.g., in the case of saturating feedback), polynomial energy decay rates are derived for strong solutions. In the final part of the thesis, we are interested in constant output regulation of a class of abstract infinite-dimensional systems governed by nonlinear contraction semigroups on Hilbert spaces. The approach we propose relies on the so-called forwarding methodology, which was originally developed for the stabilization of finite-dimensional nonlinear cascade systems. We give sufficient conditions for the existence of a dynamic control law that steers the system to some equilibrium at which the output coincides with the reference. These conditions are then investigated in the particular case of semilinear systems and illustrated by examples.

Key Words: Stabilization, Output regulation, Partial differential equations, Wave equation, Saturation, Contraction semigroups.

Doctoral School: ED EEATS - Electronics, Electrical Energy, Automatic Control, Signal Processing
Research laboratory: Grenoble Images Parole Signal Automatique (GIPSA-lab - CNRS/Grenoble INP-UGA/UGA)
Thesis supervision: Christophe PRIEUR and Francesco FERRANTE

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Updated on  June 2, 2023