Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions-Reference-Cited by-同舟云学术

Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

Published:2021-12-01 Issue:4 Volume:50 Page:427-455
ISSN:2720-4278
Container-title:Control and Cybernetics
language:en
Short-container-title:

Author:

Krug Richard¹,Leugering Günter¹,Martin Alexander¹,Schmidt Martin²,Weninger Dieter¹

Affiliation:

1. Friedrich-Alexander-Universität Erlangen-Nürnberg , Department of Data Science , Cauerstr. 11 , Erlangen , Germany

2. Trier University , Department of Mathematics , Universitätsring 15 , Trier , Germany

Abstract

Abstract In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/candc-2021-0026

Reference31 articles.

1. Barker, A. T. and Stoll, M. (2015) Domain decomposition in time for PDE-constrained optimization. In: Computer Physics Communications 197, 136–143. doi: 10.1016/j.cpc.2015.08.025.

2. Bastin, G. and Coron, J.-M. (2016) Stability and Boundary Stabilization of 1-D Hyperbolic Systems, 88. Progress in Nonlinear Differential Equations and their Applications. Subseries in Control. Birkhäuser/Springer, doi: 10.1007/978-3-319-32062-5.

3. Benamou, J.-D. (1996) A domain decomposition method with coupled transmission conditions for the optimal control of systems governed by elliptic partial differential equations. SIAM Journal on Numerical Analysis 33(6), 2401–2416. doi: 10.1137/S0036142994267102.

4. Casas, E. and Fernández, L. A. (1989) A GreenâĂŹs formula for quasilinear elliptic operators. Journal of Mathematical Analysis and Applications 142(1), 62–73. doi: 10.1016/0022-247X(89)90164-9.

5. Gander, M. J. and Kwok, F. (2016) Schwarz methods for the time-parallel solution of parabolic control problems. Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, 104. Springer, Cham, 207–216. doi: 10.1007/978-3-319-18827-0_19.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems;INFORMS Journal on Computing;2023-10-18

2. Time-Domain Decomposition for Mixed-Integer Optimal Control Problems;Applied Mathematics & Optimization;2023-03-13

3. Gas Transport Network Optimization: PDE-Constrained Models;Encyclopedia of Optimization;2023

4. Nonoverlapping domain decomposition and virtual controls for optimal control problems of p-type on metric graphs;Handbook of Numerical Analysis;2023