TY - JOUR
T1 - Approximate robust output regulation of boundary control systems
AU - Humaloja, Jukka Pekka
AU - Kurula, Mikael
AU - Paunonen, Lassi
PY - 2019/6
Y1 - 2019/6
N2 - 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.
AB - 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.
KW - Controlled wave equation
KW - Distributed parameter systems
KW - Linear systems
KW - Robust control
U2 - 10.1109/TAC.2018.2884676
DO - 10.1109/TAC.2018.2884676
M3 - Article
VL - 64
SP - 2210
EP - 2223
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 6
ER -