<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>mixed</italic> 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 <italic>virtual control</italic> problems on smaller time domains.</p>
</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.

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

Friedrich-Alexander-Universität Erlangen-Nürnberg

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth...

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

Published Online: Jun 27, 2022

Page range: 427 - 455

Received: Jul 01, 2021

Accepted: Nov 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0026

Keywords
time-domain decomposition, optimal control, semilinear hyperbolic systems, convergence

© 2021 Richard Krug et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jun 27, 2022

Page range: 427 - 455

Received: Jul 01, 2021

Accepted: Nov 01, 2021

DOI: https://doi.org/10.2478/candc-2021-0026

Keywordstime-domain decomposition, optimal control, semilinear hyperbolic systems, convergence

© 2021 Richard Krug et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
time-domain decomposition, optimal control, semilinear hyperbolic systems, convergence