Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls

Lucas Bonifacius; Konstantin Pieper; Boris Vexler

doi:10.1137/18M1213816

Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls

Lucas Bonifacius
, Konstantin Pieper
, Boris Vexler

Chair of Optimal Control

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially, the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.

Original language	English
Pages (from-to)	1730-1756
Number of pages	27
Journal	SIAM Journal on Control and Optimization
Volume	57
Issue number	3
DOIs	https://doi.org/10.1137/18M1213816
State	Published - 2019

Keywords

Bang-bang controls
Error estimates
Galerkin method
Time-optimal control

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10.1137/18M1213816

Cite this

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title = "Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls",

abstract = "In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially, the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.",

keywords = "Bang-bang controls, Error estimates, Galerkin method, Time-optimal control",

author = "Lucas Bonifacius and Konstantin Pieper and Boris Vexler",

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AU - Bonifacius, Lucas

AU - Pieper, Konstantin

AU - Vexler, Boris

PY - 2019

Y1 - 2019

N2 - In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially, the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.

AB - In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially, the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.

KW - Bang-bang controls

KW - Error estimates

KW - Galerkin method

KW - Time-optimal control

UR - https://www.scopus.com/pages/publications/85070720530

U2 - 10.1137/18M1213816

DO - 10.1137/18M1213816

M3 - Article

AN - SCOPUS:85070720530

SN - 0363-0129

VL - 57

SP - 1730

EP - 1756

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 3

ER -

Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls

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Keywords

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