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Nonlinear differential encounter-evasion games with delay. (English. Russian original) Zbl 0648.90107
Cybernetics 23, No. 3, 418-425 (1987); translation from Kibernetika 1987, No. 3, 109-113 (1987).
Summary: We investigate the problem of avoiding encounter from a specified initial point (encounter-evasion problem) as described by a differential equation with delay in the state vector and its derivative. We derive different conditions for the possibility of evasion, and we find a guaranteed lower bound for the distance from the phase point to the endset.
MSC:
91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
91A99 Game theory
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[1] M. S. Nikol’skii, ?Linear differential game of encounter-evasion in the presence of delays,? Prikl. Mat. Program, No. 12, 103?112 (1974).
[2] A. A. Chikrii and G. Ts. Chikrii, ?Differential-difference game of encounter-evasion,? Prikl. Mat. Program., No. 6, 995?1002 (1976).
[3] V. V. Ostapenko an A. P. Yakovleva, ?Encounter-evasion problem with a delayed argument,? Avtomat. Telemekhan., No. 8, 10?14 (1981).
[4] N. Yu. Satimov and B. B. Rikhsiev, ?Quasilinear differential games of encounter-evasion,? Differents. Uravn,14, No. 6, 1046?1052 (1978).
[5] N. Yu. Satimov, ?Nonlinear differential game of encounter-evasion,? Mat. Zametki,21, No. 3, 415?425 (1977).
[6] N. Yu. Satimov, ?Theory of differential games of encounter-evasion,? Mat. Sb.,103, No. 3, 430?444 (1977).
[7] N. Yu. Satimov, ?Some generalizations of Pontryagin’s lemma of squares,? Differents. Uravn.,20, No. 9, 1548?1555 (1984).
[8] N. Yu. Satimov and B. B. Rikhsiev, ?Linear differential games of encounter-evasion with integral constraints,? Differents. Uravn.,18, No. 4, 599?608 (1982).
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