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A Partial Internal Model for Approximate Robust Output Regulation of Boundary Control Systems

Research output: Chapter in Book/Report/Conference proceedingConference contributionProfessional


Original languageEnglish
Title of host publication23rd International Symposium on Mathematical Theory of Networks and Systems
Number of pages6
Publication statusPublished - 20 Jul 2018
Publication typeD3 Professional conference proceedings
EventInternational Symposium on Mathematical Theory of Networks and Systems - The Hong Kong University of Science and Technology, Hong Kong, Hong Kong
Duration: 16 Jul 201820 Jul 2018


ConferenceInternational Symposium on Mathematical Theory of Networks and Systems
Abbreviated titleMTNS
CountryHong Kong
CityHong Kong
Internet address


Introduced for finite-dimensional systems by Fran- cis and Wonham in the mid 70’s, the internal model principle states that a stabilizing controller achieves asymptotic output tracking and disturbance rejection robustly if and only if it contains a p-copy of the exosystem frequencies, where p is the dimension of the output space of the plant. Later, the internal model principle has been extended, e.g., to boundary control systems on multidimensional spatial domains, and in this setting it follows from the principle that every robust output regulator is necessarily infinite-dimensional. However, it was recently established by the authors that robust approximate output tracking can be achieved with a finite-dimensional controller, and in the present paper, we formulate an internal model for this purpose. The efficiency of the method is numerically demonstrated using the heat equation on the unit square in $\mathbb{R}^2$ with boundary control and boundary observation.

Field of science, Statistics Finland