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Reduced Order Controller Design for Robust Output Regulation

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Original languageEnglish
Pages (from-to)2480-2493
JournalIEEE Transactions on Automatic Control
Issue number6
Early online date22 Jul 2019
Publication statusPublished - Jun 2020
Publication typeA1 Journal article-refereed


We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on a Galerkin approximation of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part of the paper we design controllers for robust output tracking and disturbance rejection for a 1D reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a 1D beam equation with Kelvin-Voigt damping.


  • Mathematical model, Method of moments, Closed loop systems, Hilbert space, Reduced order systems, Adaptive control, Robust output regulation, partial differential equation, controller design, Galerkin approximation, model reduction

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