# zbMATH — the first resource for mathematics

Differential games of evasion with many pursuers. (English) Zbl 0679.90110
Summary: We extend the method of W. Rzymowski [“Method of construction of the evasion strategy for differential games with many pursuers”, Diss. Math. 247 (1986; Zbl 0597.90106)] to the general case, i.e., to games governed by an equation of the form $$z'=f(t,z,u,v)$$, where the terminal set is a finite union of linear subspaces of the state space. We prove a theorem providing a new sufficient condition for avoidance of many pursuers that is more general than previous ones. To apply this method to such a general case, we introduce a new strategy for the evader; however, use of similar strategies from Rzymowski is also possible. After obtaining this result, we find a similar condition concerning games governed by many differential equations. Last we consider games described by kth order differential inclusions. For such games (with many pursuers) we give a new sufficient condition for “evasion along each trajectory of a certain set.”

##### MSC:
 91A24 Positional games (pursuit and evasion, etc.) 91A23 Differential games (aspects of game theory) 91A99 Game theory
Full Text:
##### References:
 [1] Borówko, P; Rzymowski, W, Avoidance of many pursuers in the simple motion case, J. math. anal. appl., 111, 535-546, (1985) · Zbl 0581.90107 [2] Chikrii, A.A, Nonlinear differential evasion games, Soviet math. dokl., 20, 591-595, (1979) · Zbl 0423.90101 [3] Chikrii, A.A, A method of variable directions in nonlinear runaway games, Kibernetika, 1, 48-54, (1984), [in Russian] [4] Chodun, W, Avoidance of many pursuers in differential games described by differential inclusions, J. math. anal. appl., 135, 581-590, (1988) · Zbl 0655.90104 [5] Chodun, W, Avoidance of many pursuers in differential games governed by kth order differential equations, J. differential equations, 76, 213-221, (1988) · Zbl 0655.90105 [6] Filippov, A.F, Differential equations with noncontinuous right-hand side, (1985), Nauka Moscow, [in Russian] · Zbl 0571.34001 [7] Pshenichny, B.N, Ε-strategies in differential games, (), 44-99 [8] Rzymowski, W, Method of construction of the evasion strategy for differential games with many pursuers, Dissertationes math., CCXLVII, (1986) · Zbl 0597.90106 [9] Rzymowski, W, Evasion along each trajectory in differential games with many pursuers, J. differential equations, 62, 334-356, (1986) · Zbl 0588.90108 [10] Rzymowski, W, Avoidance of one pursuer, J. math. anal. appl., 120, 89-94, (1986) · Zbl 0641.90109 [11] Zak, V.L, Construction of an evasion strategy from many pursuers for dynamical systems, Tekh. kibernet., 4, 143-147, (1984), [in Russian] [12] Zak, V.L, Strategy of evasion from many pursuers, Optimal control appl. methods, 7, 389-410, (1986) · Zbl 0597.90110
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.