TIME-DOMAIN DECOMPOSITION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR HYPERBOLIC SYSTEMS

Krug R, Leugering G, Martin A, Schmidt M, Weninger D (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Book Volume: 59

Pages Range: 4339-4372

Journal Issue: 6

DOI: 10.1137/20M138329X

Abstract

In this article, we extend the time-domain decomposition method described by Lagnese and Leugering [Systems Control Lett., 48 (2003), pp. 229--242] to semilinear optimal control problems for hyperbolic balance laws with spatio-temp oral varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis is done entirely on the continuous level. A distinguishing feature of the method is that the decomposed optimality system can be interpreted as an optimality system of a local ``virtual"" optimal control problem. Thus, the iterative time-domain decomposition of the optimality system can be interpreted as an iterative parallel scheme for virtual optimal control problems on the subintervals. A typical example and further comments are given to show the range of potential applications. Moreover, we provide some numerical experiments to give a first interpretation of the role of the parameters involved in the iterative process.

Authors with CRIS profile

Involved external institutions

Universität Trier Germany (DE)

How to cite

APA:

Krug, R., Leugering, G., Martin, A., Schmidt, M., & Weninger, D. (2021). TIME-DOMAIN DECOMPOSITION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR HYPERBOLIC SYSTEMS. SIAM Journal on Control and Optimization, 59(6), 4339-4372. https://doi.org/10.1137/20M138329X

MLA:

Krug, Richard, et al. "TIME-DOMAIN DECOMPOSITION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR HYPERBOLIC SYSTEMS." SIAM Journal on Control and Optimization 59.6 (2021): 4339-4372.

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