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

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
Externally published	Yes

Funding

∗Received by the editors September 13, 2018; accepted for publication (in revised form) March 18, 2019; published electronically May 21, 2019. http://www.siam.org/journals/sicon/57-3/M121381.html Funding: The first author gratefully acknowledges support from the International Research Training Group (IGDK), funded by the German Science Foundation (DFG), and the Austrian Science Fund (FWF). The second author acknowledges funding by the US Department of Energy Office of Science grant DE-SC0016591 and by the US Air Force Office of Scientific Research grant FA9550-15-1-0001. †Fakultät für Mathematik, Technische Universität München, Munich, Germany (lucas. [email protected], [email protected]). ‡Department of Scientific Computing, Florida State University, Tallahassee, FL 32306 (kpieper@ fsu.edu). The first author gratefully acknowledges support from the International Research Training Group (IGDK), funded by the German Science Foundation (DFG), and the Austrian Science Fund (FWF). The second author acknowledges funding by the US Department of Energy Office of Science grant DE-SC0016591 and by the US Air Force Office of Scientific Research grant FA9550- 15-1-0001.

Keywords

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

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10.1137/18M1213816

Cite this

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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.",

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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.

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KW - Galerkin method

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

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