TY - GEN
T1 - Constructive finite-dimensional observer-based boundary control of stochastic parabolic PDEs
AU - Wang, Pengfei
AU - Katz, Rami
AU - Fridman, Emilia
N1 - Publisher Copyright:
© 2022 American Automatic Control Council.
PY - 2022
Y1 - 2022
N2 - Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs has been suggested by employing a modal decomposition approach. In the present paper, we aim to extend this method to the stochastic parabolic PDEs with nonlinear multiplicative noise. We consider the Neumann actuation and boundary measurement via dynamic extension. The controller dimension is defined by N0 unstable modes, whereas the observer may have a larger dimension N. We provide mean-square L2 stability analysis of the full-order closed-loop system leading to linear matrix inequality (LMI) conditions for finding N. We prove that the LMIs are always feasible for small enough noise intensity and large enough N. A numerical example demonstrates the efficiency of our method.
AB - Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs has been suggested by employing a modal decomposition approach. In the present paper, we aim to extend this method to the stochastic parabolic PDEs with nonlinear multiplicative noise. We consider the Neumann actuation and boundary measurement via dynamic extension. The controller dimension is defined by N0 unstable modes, whereas the observer may have a larger dimension N. We provide mean-square L2 stability analysis of the full-order closed-loop system leading to linear matrix inequality (LMI) conditions for finding N. We prove that the LMIs are always feasible for small enough noise intensity and large enough N. A numerical example demonstrates the efficiency of our method.
UR - http://www.scopus.com/inward/record.url?scp=85138489771&partnerID=8YFLogxK
U2 - 10.23919/ACC53348.2022.9867400
DO - 10.23919/ACC53348.2022.9867400
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AN - SCOPUS:85138489771
T3 - Proceedings of the American Control Conference
SP - 1667
EP - 1672
BT - 2022 American Control Conference, ACC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 American Control Conference, ACC 2022
Y2 - 8 June 2022 through 10 June 2022
ER -