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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.”

91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
91A99 Game theory
Full Text: DOI
[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
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