Skip Navigation

Applied Mathematics Research eXpress (2008) Vol. 2008 : article ID abm012, 49 pages, doi:10.1093/amrx/abm012 published on January 30, 2008
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Glizer, V. Y.
Right arrow Articles by Turetsky, V.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls

Valery Y. Glizer1,2, and Vladimir Turetsky1

1 Faculty of Aerospace Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel
2 Department of Mathematics, Ort Braude Academic College of Engineering, P.O.B. 78, Karmiel 21982, Israel

Correspondence: Correspondence to be sent to: Vladimir Turetsky, Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel. e-mail: turetsky{at}aerodyne.technion.ac.il

A zero-sum finite-horizon differential game with linear dynamics and bounded controls is considered. The target set is a given hyperplane in the state space. The cost function is the distance between the terminal state and this hyperplane. The complete game solution is obtained in two classes of controls: open-loop and feedback-based controls.



References

  1. Isaacs R. Differential Games (1965) New York: John Wiley.
  2. Blaquiere A., Gerard F., Leitmann G. Quantitative and Qualitative Games (1969) New York: Academic Press.
  3. Krasovskii N., Subbotin A. Game-Theoretical Control Problems (1988) New York: Springer.
  4. Lewin J. Differential Games (1994) London: Springer.
  5. Basar T., Bernhard P. H{infty}-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (1995) Boston, MA: Birkhauser.
  6. Bryson A., Ho Y. Applied Optimal Control (1975) New York: Hemisphere.
  7. Gutman S. On optimal guidance for homing missiles. Journal of Guidance and Control (1979) 2:296–300.
  8. Shinar J. Solution techniques for realistic pursuit-evasion games. In: Advances in Control and Dynamic Systems—Leondes C., ed. (1981) 17. New York: Academic Press. 63–124.
  9. Krasovskii N. Control of a Dynamic System [in Russian] (1985) Moscow: Nauka.
  10. Shima T., Shinar J. Time-varying linear pursuit-evasion game models with bounded controls. Journal of Guidance, Control and Dynamics (2002) 25:425–32.[ISI]
  11. Ho Y. C., Bryson A. E., Baron S. Differential games and optimal pursuit-evasion strategies. IEEE Transactions on Automatic Control (1965) AC-10:385–9.[CrossRef]
  12. Petrosjan L. Differential Games of Pursuit (1993) Singapore: World Scientific.
  13. Turetsky V., Shinar J. Missile guidance laws based on pursuit-evasion game formulations. Automatica (2003) 39:607–18.[CrossRef][ISI]
  14. Turetsky V., Glizer V. Continuous feedback control strategy with maximal capture zone in a class of pursuit games. International Game Theory Review (2005) 7:1–24.[CrossRef]
  15. Patsko V. Switching surfaces in linear differential games with fixed termination time. Journal of Applied Mathematics and Mechanics (2004) 68:583–95.[CrossRef]
  16. Kumkov S., Patsko V., Shinar J. On level sets with "Narrow Throats" in linear differential games. International Game Theory Review (2005) 7:285–311.[CrossRef]
  17. Karlin S. Mathematical Methods and Theory in Games, Programming and Economics (1959) Reading, MA: Addison-Wesley.

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Glizer, V. Y.
Right arrow Articles by Turetsky, V.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?