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

Gugat M, Leugering G (2002)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2002

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 22

Pages Range: 151-192

Journal Issue: 2

URI: http://link.springer.com/article/10.1023/A:1015472323967

DOI: 10.1023/A:1015472323967

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.

Authors with CRIS profile

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://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: Download