Structure of Viability Kernels for Some Linear Differential Games

N. D. Botkin () and E. A. Ryazantseva
Additional contact information
N. D. Botkin: Technische Universität München
E. A. Ryazantseva: Ural Department of Russian Academy of Sciences

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 1, No 3, 42-57

Abstract: Abstract A convenient form of necessary and sufficient conditions of viability for differential games with linear dynamics is proposed. These conditions are utilized to construct maximal viable subsets of state constraints, viability kernels, in two illustrative two-dimensional examples. These examples demonstrate the relative simplicity of the structure of the viability kernels. It was found that the boundaries of the viability kernels consist of segments of the boundary of the state constraint and of lines defined by the first integrals of the governing equations as the players use extremal constant controls. It is conjectured that such a structure holds in high dimensional cases too.

Keywords: Linear differential games; Viability kernels; Exact solutions (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-010-9706-1 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:147:y:2010:i:1:d:10.1007_s10957-010-9706-1

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

DOI: 10.1007/s10957-010-9706-1

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 ().