This volume lays the mathematical foundations for the theory of differential games, developing a rigorous mathematical framework with existence theorems. Topics include games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, and games with restricted phase coordinates. 1971 edition.
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5-strategy A6 5-values associated with 1.1 assume called compact subsets complete the proof concept consider continuous function continuously differentiable control sets define denote differential equations differential game associated differential system Euclidean spaces existence of value extended value fixed duration follows Friedman 20 G Rm game of fixed games of survival H+(t Hamilton-Jacobi equation Hamilton-Jacobi theory Hence hold inequality inf sup initial conditions interval Isaacs equation Lemma Lipschitz continuous loop equilibrium strategy lower 5-strategy lower values max f(t measurable functions modify partial differential equations payoff P(y payoff set player positive number proof of Theorem proved pursuit-evasion game Remark saddle point satisfies Similarly solution stochastic control Stochastic differential games sufficiently small sup inf Suppose synthesis Theorem 3.1 trajectory corresponding trajectory x(t tries to maximize upper 5-strategy upper and lower V(QE V+(QE V+(t Varaiya vector X Rm x0 G