TY - JOUR

T1 - Sub-Predictors and Classical Predictors for Finite-Dimensional Observer-Based Control of Parabolic PDEs

AU - Katz, Rami

AU - Fridman, Emilia

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2022

Y1 - 2022

N2 - We study constant input delay compensation by using finite-dimensional observer-based controllers in the case of the 1D heat equation. We consider Neumann actuation with nonlocal measurement and employ modal decomposition with $N+1$ modes in the observer. We introduce a chain of $M$ sub-predictors that leads to a closed-loop ODE system coupled with infinite-dimensional tail. Given an input delay $r$ , we present LMI stability conditions for finding $M$ and $N$ and the resulting exponential decay rate and prove that the LMIs are always feasible for any $r$. We also consider a classical observer-based predictor and show that the corresponding LMI stability conditions are feasible for any $r$ provided $N$ is large enough. A numerical example demonstrates that the classical predictor leads to a lower-dimensional observer. However, it is known to be hard for implementation due to the distributed input signal.

AB - We study constant input delay compensation by using finite-dimensional observer-based controllers in the case of the 1D heat equation. We consider Neumann actuation with nonlocal measurement and employ modal decomposition with $N+1$ modes in the observer. We introduce a chain of $M$ sub-predictors that leads to a closed-loop ODE system coupled with infinite-dimensional tail. Given an input delay $r$ , we present LMI stability conditions for finding $M$ and $N$ and the resulting exponential decay rate and prove that the LMIs are always feasible for any $r$. We also consider a classical observer-based predictor and show that the corresponding LMI stability conditions are feasible for any $r$ provided $N$ is large enough. A numerical example demonstrates that the classical predictor leads to a lower-dimensional observer. However, it is known to be hard for implementation due to the distributed input signal.

KW - Distributed parameter systems

KW - observer-based control

KW - time-delay

UR - http://www.scopus.com/inward/record.url?scp=85107195950&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2021.3084525

DO - 10.1109/LCSYS.2021.3084525

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AN - SCOPUS:85107195950

SN - 2475-1456

VL - 6

SP - 626

EP - 631

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

M1 - 9442823

ER -