Skip to main content
SpringerLink
Log in

Characterizations of the values of differential games

  • Published:
Applied Mathematics and Optimization Submit manuscript

Abstract

The upper and lower directional derivates of the value function of a differential game are shown to satisfy certain relationships. These relationships imply that the value is a viscosity solution of the Isaacs equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barron EN, Evans LC, Jensen R (1984) Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls. J Differential Equations 53:213–233

    Google Scholar 

  2. Berkovitz LD (1985) The existence of value and saddle point in games of fixed duration. SIAM J Control Optim 23:172–196

    Google Scholar 

  3. Berkovitz LD (1986) Differential games of generalized pursuit and evasion. SIAM J Control 24:361–373

    Google Scholar 

  4. Elliott RJ, Kalton NJ (1972) The existence of value in differential games. Mem Amer Math Soc 126

  5. Evans LC, Souganidis PE (1984) Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations. Indiana Univ Math J 33:773–795

    Google Scholar 

  6. Fleming WH (1964) The Convergence Problem for Differential Games, II. Annals of Mathematics Study, No. 52. Princeton University Press, Princeton, NJ, pp 195–210

    Google Scholar 

  7. Friedman A (1971) Differential Games. Wiley-Interscience, New York

    Google Scholar 

  8. Friedman A (1974) Differential Games. CBMS Regional Conference Series in Mathematics, No. 18. American Mathematical Society, Providence, RI

    Google Scholar 

  9. Ishi H (1984) Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Indiana Univ Math J 33:721–748

    Google Scholar 

  10. Krasovskii NN, Subbotin AI (1974) Positional Differential Games. Nauka, Moscow

    Google Scholar 

  11. Lions P-L, Souganidis PE (1985) Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations. SIAM J Control Optim 23:566–583

    Google Scholar 

  12. Souganidis PE (1983) Thesis, University of Wisconsin

  13. Subbotin AI (1984) Generalization of the main equation of differential game theory. J Optim Theory Appl 43:103–134

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purdue University, 47907, West Lafayette, Indiana, USA

    Leonard D. Berkovitz

Authors
  1. Leonard D. Berkovitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by W. Fleming

This research was performed under NSF Grant No. DMS-8500353.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkovitz, L.D. Characterizations of the values of differential games. Appl Math Optim 17, 177–183 (1988). https://doi.org/10.1007/BF01448365

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01448365

Keywords

Search

Navigation