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High-gain observer design for systems of PDEs

Abstract : This thesis introduces some non-trivial extensions of the classical high-gain observer design for finite-dimensional nonlinear systems to some classes of infinite-dimensional systems, written as triangular systems of coupled partial differential equations (PDEs), where an observation of one coordinate of the state along the spatial domain is considered as system's output. To deal with this problem, depending on a property of the differential operator associated to each system of PDEs, direct and indirect observer design is proposed. First, via direct observer design, solvability of this high-gain observer design problem is proven for a class of systems of quasilinear hyperbolic partial integro-differential equations of balance laws with a single characteristic velocity. Then, for the case of distinct velocities, indirect observer design is proposed for a class of 2x2 quasilinear and a class of nxn linear inhomogeneous hyperbolic systems. This design is also applied to semilinear reaction-diffusion systems of 2 and 3 equations. The indirect design introduces infinite-dimensional state transformations of the considered systems to target systems of PDEs and this leads to the injection of spatial derivatives of the output in the observer dynamics. The convergence of the proposed observers in appropriate regularity space norms is based upon various introduced Lyapunov tools. The thesis also addresses the application of the proposed theoretical results to epidemic models, chemical reactors, and diffusional Lotka-Volterra systems. Finally, the proposed observer designs are applied to the output feedback stabilization of a cascade system of linear Korteweg-de Vries equations, where two different boundary control problems are considered.
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Submitted on : Tuesday, January 5, 2021 - 2:09:07 PM
Last modification on : Friday, March 25, 2022 - 9:40:56 AM
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  • HAL Id : tel-03097631, version 1


Constantinos Kitsos. High-gain observer design for systems of PDEs. Automatic Control Engineering. Université Grenoble Alpes [2020-..], 2020. English. ⟨NNT : 2020GRALT031⟩. ⟨tel-03097631⟩



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