A Study on Abnormality in Variational and Optimal Control Problems

C. Bruni and D. Iacoviello
Additional contact information
C. Bruni: Università di Roma – La Sapienza
D. Iacoviello: Università di Roma – La Sapienza

Journal of Optimization Theory and Applications, 2004, vol. 121, issue 1, No 3, 64 pages

Abstract: Abstract In this paper, a variational problem is considered with differential equality constraints over a variable interval. It is stressed that the abnormality is a local character of the admissible set; consequently, a definition of regularity related to the constraints characterizing the admissible set is given. Then, for the local minimum necessary conditions, a compact form equivalent to the well-known Euler equation and transversality condition is given. By exploiting this result and the previous definition of regularity, it is proved that nonregularity is a necessary and sufficient condition for an admissible solution to be an abnormal extremal. Then, a necessary and sufficient condition is given for an abnormal extremal to be weakly abnormal. The analysis of the abnormality is completed by considering the particular case of affine constraints over a fixed interval: in this case, the abnormality turns out to have a global character, so that it is possible to define an abnormal problem or a normal problem. The last section is devoted to the study of an optimal control problem characterized by differential constraints corresponding to the dynamics of a controlled process. The above general results are particularized to this problem, yielding a necessary and sufficient condition for an admissible solution to be an abnormal extremal. From this, a previously known result is recovered concerning the linearized system controllability as a sufficient condition to exclude the abnormality.

Keywords: Calculus of variations; optimal control problems; abnormal extremals (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/B:JOTA.0000026130.86491.22 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026130.86491.22

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/B:JOTA.0000026130.86491.22

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().