zbMATH — the first resource for mathematics

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.
91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
91A99 Game theory
Full Text: DOI
[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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.