Dynamic output-based feedback stabilizability for linear parabolic equations with memory

Fuente: arXiv
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Main Authors: Khan, Arbaz, Mahajan, Sumit, Rodrigues, Sérgio S.
Format: Preprint
Published: 2025
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_version_ 1866909596682027008
author Khan, Arbaz
Mahajan, Sumit
Rodrigues, Sérgio S.
author_facet Khan, Arbaz
Mahajan, Sumit
Rodrigues, Sérgio S.
contents The stabilizability of a general class of linear parabolic equations with a memory term, is achieve by explicit output feedback. The control input is given as a function of a state-estimate provided by an exponential dynamic Luenberger observer based on the output of sensor measurements. The numbers of actuators and sensors are finite. The feedback input and output injection operators are given explicitly involving appropriate orthogonal projections. For exponential kernels, exponential stabilizability can be achieved with the rate of the exponential kernel. The discretization and simulation of the controlled systems are addressed as well and results of simulations are reported showing the performance of the proposed dynamic output-based control feedback input. We include simulations for both exponential and weakly singular Riesz kernels, showing the success of the strategy in obtaining a stabilizing input.
format Preprint
id arxiv_https___arxiv_org_abs_2504_20235
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Dynamic output-based feedback stabilizability for linear parabolic equations with memory
Khan, Arbaz
Mahajan, Sumit
Rodrigues, Sérgio S.
Optimization and Control
Analysis of PDEs
The stabilizability of a general class of linear parabolic equations with a memory term, is achieve by explicit output feedback. The control input is given as a function of a state-estimate provided by an exponential dynamic Luenberger observer based on the output of sensor measurements. The numbers of actuators and sensors are finite. The feedback input and output injection operators are given explicitly involving appropriate orthogonal projections. For exponential kernels, exponential stabilizability can be achieved with the rate of the exponential kernel. The discretization and simulation of the controlled systems are addressed as well and results of simulations are reported showing the performance of the proposed dynamic output-based control feedback input. We include simulations for both exponential and weakly singular Riesz kernels, showing the success of the strategy in obtaining a stabilizing input.
title Dynamic output-based feedback stabilizability for linear parabolic equations with memory
topic Optimization and Control
Analysis of PDEs
url https://arxiv.org/abs/2504.20235