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Approximate robust output regulation of boundary control systems

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)2210-2223
JournalIEEE Transactions on Automatic Control
Issue number6
Early online date2018
Publication statusPublished - Jun 2019
Publication typeA1 Journal article-refereed


We extend the internal model principle for systems with boundary control and boundary observation, and construct a robust controller for this class of systems. However, as a consequence of the internal model principle, any robust controller for a plant with infinite-dimensional output space necessarily has infinite-dimensional state space. We proceed to formulate the approximate robust output regulation problem and present a finite-dimensional controller structure to solve it. Our main motivating example is a wave equation on a bounded multidimensional spatial domain with force control and velocity observation at the boundary. In order to illustrate the theoretical results, we construct an approximate robust controller for the wave equation on an annular domain and demonstrate its performance with numerical simulations.


  • Controlled wave equation, Distributed parameter systems, Linear systems, Robust control

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Field of science, Statistics Finland

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