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International Journal of Game Theory

, Volume 34, Issue 4, pp 495–527 | Cite as

Zero-sum state constrained differential games: existence of value for Bolza problem

  • Piernicola BettiolEmail author
  • Pierre Cardaliaguet
  • Marc Quincampoix
Original Article

Abstract

We prove the existence of a lower semicontinuous value function for Bolza problem in differential games with state-constraints. As a byproduct, we obtain a new estimation of trajectories of a control system by trajectories with state constraints. This result which could be interesting by itself enables us to build a suitable strategy for constrained differential games. We also characterize the value function by means of viscosity solutions and give conditions under which the value function is locally Lipschitz continuous.

Keywords

Differential games Bolza problem State constraints Viability Theory 

AMS Classification

49N70 90D25 

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Copyright information

© Springer Verlag 2006

Authors and Affiliations

  • Piernicola Bettiol
    • 1
    Email author
  • Pierre Cardaliaguet
    • 2
  • Marc Quincampoix
    • 2
  1. 1.SISSA/ISASTriesteItaly
  2. 2.Département de MathématiquesUniversité de Bretagne OccidentaleBrestFrance

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