Abstract
In this paper we consider the classical problem of pursuit and evasion for continuous-time and discrete-time systems. We prove the convergence, as the time step goes to 0, of the upper and lower value functions of the discrete-time game to the upper and lower values of the differential game. This is done assuming a capturability condition either on the differential game, or on the discrete-time game uniformly for small values of the time step. An application is the existence of the value in the sense of Fleming under rather general conditions.
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Bardi, M., Soravia, P. (1991). Approximation of differential games of pursuit-evasion by discrete-time games. In: Hämäläinen, R.P., Ehtamo, H.K. (eds) Differential Games — Developments in Modelling and Computation. Lecture Notes in Control and Information Sciences, vol 156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040234
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DOI: https://doi.org/10.1007/BFb0040234
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