On Norm and Time Optimal Controls for Systems Described by Linear Parabolic PDEs

This work proposes a general theory of norm and time optimal control for a class of null controllable systems. We provide sufficient conditions for the existence and uniqueness of optimal controls, the bang-bang property and for the equivalence between norm and time optimal control problems. The obtained abstract theorems allow us to obtain several new results for systems described by parabolic PDEs, with distributed or boundary controls.

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Publication Details

Journal
SIAM Journal on Control and Optimization
Published
2025-01-23
DOI
https://doi.org/10.1137/24m1671852
Primary Topic
Stability and Controllability of Differential Equations
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
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article

On Norm and Time Optimal Controls for Systems Described by Linear Parabolic PDEs

Marius Tucsnak
SIAM Journal on Control and Optimization
Stability and Controllability of Differential Equations
article

On Norm and Time Optimal Controls for Systems Described by Linear Parabolic PDEs

Marius Tucsnak
article en

Abstract

This work proposes a general theory of norm and time optimal control for a class of null controllable systems. We provide sufficient conditions for the existence and uniqueness of optimal controls, the bang-bang property and for the equivalence between norm and time optimal control problems. The obtained abstract theorems allow us to obtain several new results for systems described by parabolic PDEs, with distributed or boundary controls.

SIAM Journal on Control and OptimizationVol. 63(1)
Centre National de la Recherche Scientifique (FR), Université de Bordeaux (FR), Institut Polytechnique de Bordeaux (FR), Institut de Mathématiques de Bordeaux (FR)
New York University Shanghai, Agence Nationale de la Recherche
Openalex Percentile: Top 100%
Stability and Controllability of Differential Equations
DOIOpen Access PDFOpenAlex
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On Norm and Time Optimal Controls for Systems Described by Linear Parabolic PDEs — Marius Tucsnak · SIAM Journal on Control and Optimization (2025) | TGRS Research Map | TGRS