Abstract
It is shown that, in differential games, strategies can be defined for the players in such a way that their controls depend, for each timet, on a finite section of the past of the trajectoryx(t). In particular,s-delay,r-memory strategies can be defined as in the Varaiya-Lin approach. It is shown that, for deterministic differential games with terminal payoff, the upper and lower values of the game so defined, are independent of the lengthr of the memory. Lettingr → 0, a feedback strategy is obtained which depends only on the present (and infinitesimal past) of the trajectoryx(t).
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Communicated by P. L. Yu
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Roxin, E.O. Feedback strategies with finite memory in differential games. J Optim Theory Appl 27, 127–134 (1979). https://doi.org/10.1007/BF00933330
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DOI: https://doi.org/10.1007/BF00933330