Abstract
A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by θ>1.P wants to reduce his distancePE fromE below the capture radius ρ. Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.
We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds θ.
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Breakwell, J. V.,Pursuit of a Faster Evader, The Theory and Application of Differential Games, Edited by J. D. Grote, D. Reidel Publishing Company, Dordrecht, Holland, 1975.
Flynn, J.,Lion and Man: The Boundary Constraint, SIAM Journal on Control, Vol. 11, pp. 397–411, 1973.
Flynn, J.,Some Results on Max-Min Pursuit, SIAM Journal on Control, Vol. 12, pp. 53–69, 1974.
Flynn, J.,Lion and Man: The General Case, SIAM Journal on Control, Vol. 12, pp. 581–597, 1974.
Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.
Breakwell, J. V.,Zero-Sum Differential Games with Terminal Payoff, Differential Games and Applications, Edited by P. Hagedorn, H. W. Knobloch, and G. J. Olsder, Springer-Verlag, Berlin, Germany, 1977.
Bernhard, P.,Singular Surfaces in Differential Games, Differential Games and Applications, Edited by P. Hagedorn, H. W. Knobloch, and G. J. Olsder, Springer-Verlag, Berlin, Germany, 1977.
Lewin, J., andOlsder, G. J.,Conic Surveillance Evasion, Journal of Optimization Theory and Applications, Vol. 27, pp. 7–125, 1979.
Basar, T., andOlsder, G. J.,Noncooperative Dynamic Game Theory, Academic Press, New York, New York, 1982.
Chigir, S. A.,The Game Problem on the Dolichobrachistochrone, PMM, Vol. 30, pp. 1003–1013, 1976.
Lewin, J.,A Note on the Uniqueness of the Value Function in Differential Games (to appear).
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Communicated by J. V. Breakwell
The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.
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Lewin, J. The lion and man problem revisited. J Optim Theory Appl 49, 411–430 (1986). https://doi.org/10.1007/BF00941070
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DOI: https://doi.org/10.1007/BF00941070