Work

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

Year: 2021

Type: article

Abstract: 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.

Source: IEEE Control Systems Letters

DOI: 10.1109/lcsys.2021.3084525

Authors: Rami Katz, Emilia Fridman

Institution: Tel Aviv University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Israel Science Foundation, Tel Aviv University

Award: G1854307505