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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Professional

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**A Partial Internal Model for Approximate Robust Output Regulation of Boundary Control Systems.** / Humaloja, Jukka-Pekka; Paunonen, Lassi; Kurula, Mikael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Professional

### Harvard

*23rd International Symposium on Mathematical Theory of Networks and Systems.*pp. 586-591, International Symposium on Mathematical Theory of Networks and Systems, Hong Kong, Hong Kong, 16/07/18.

### APA

*23rd International Symposium on Mathematical Theory of Networks and Systems*(pp. 586-591)

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TY - GEN

T1 - A Partial Internal Model for Approximate Robust Output Regulation of Boundary Control Systems

AU - Humaloja, Jukka-Pekka

AU - Paunonen, Lassi

AU - Kurula, Mikael

PY - 2018/7/20

Y1 - 2018/7/20

N2 - 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.

AB - 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.

M3 - Conference contribution

SP - 586

EP - 591

BT - 23rd International Symposium on Mathematical Theory of Networks and Systems

ER -