Regularization of L-∞ optimal control problems for distributed parameter systems

Journal article
(Original article)


Publication Details

Author(s): Gugat M, Leugering G
Journal: Computational Optimization and Applications
Publisher: Springer Verlag (Germany)
Publication year: 2002
Volume: 22
Journal issue: 2
Pages range: 151-192
ISSN: 0926-6003
Language: English


Abstract


We consider L -norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.



In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.



The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.



FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Gugat, M., & Leugering, G. (2002). Regularization of L-∞ optimal control problems for distributed parameter systems. Computational Optimization and Applications, 22(2), 151-192. https://dx.doi.org/10.1023/A:1015472323967

MLA:
Gugat, Martin, and Günter Leugering. "Regularization of L-∞ optimal control problems for distributed parameter systems." Computational Optimization and Applications 22.2 (2002): 151-192.

BibTeX: 

Last updated on 2018-09-08 at 06:38