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On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems

Submission Status:epub ahead of print
  • We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval (0,T) that depends on the boundary traces of the solution. If the time horizon T is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for T to infinity the approximation error converges to zero in the sense of the norm in L^2(0,1) with the rate 1/T, if the time interval (0,T) is transformed to the fixed interval (0,1). Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If T is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations.

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Metadaten
Author:Martin Gugat, Falk Hante
DOI:https://doi.org/10.1137/17M1134470
Parent Title (English):SIAM Journal on Control and Optimization
Document Type:Article
Language:English
Date of Publication (online):2019/02/01
Date of first Publication:2019/02/06
Release Date:2019/02/06
Volume:57
Issue:1
First Page:264
Last Page:289
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:A03
C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International