The Pontryagin Maximum Principle for Nonlinear Optimal Control Problems with Infinite Horizon

Nico Tauchnitz ()
Additional contact information
Nico Tauchnitz: BTU Cottbus-Senftenberg

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 2, 27-48

Abstract: Abstract The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this paper, we follow the approach to state the optimal control problem as an extremal problem in function spaces, and then realizing the Lagrange principle for this extremal problem via the separation technique. The result is the Pontryagin maximum principle as necessary condition for a strong local minimizer in infinite horizon optimal control problems. This approach yields the existence of the adjoint and the validity of the transversality conditions at infinity. To get the Lagrange multipliers rule in this particular context, we introduce a multiple needle variation technique on the infinite horizon.

Keywords: Pontryagin maximum principle; Optimal control; Infinite horizon; Transversality conditions; 46E15; 46E35; 49K15 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0723-y 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:167:y:2015:i:1:d:10.1007_s10957-015-0723-y

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

DOI: 10.1007/s10957-015-0723-y

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 ().