This volume lays the mathematical foundations for the theory of differential games, developing a rigorous mathematical framework with existence theorems. It begins with a precise definition of a differential game and advances to considerations of games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, and games with restricted phase coordinates. Final chapters cover selected topics (including capturability and games with delayed information) and N-person games.
Geared toward graduate students, Differential Games will be of particular interest to professionals in the fields of electrical engineering, industrial engineering, economics, and mathematics. Although intended primarily for self-study, it can be used as a core or ancillary text in courses in differential games, game theory, and control theory.
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analogous assertion associated with l.2.l assume assumption bounded set bounded subsets called chooses closed domain compact subsets completes the proof Compute conclude conditions A1)—(A3 Consider the differential constant independent continuous function continuously differentiable control functions control sets convex set deﬁned deﬁnition denote differential equations differential game associated differential system diﬂerential equilibrium point exists ﬁnd ﬁrst ﬁxed duration game given game of pursuit-evasion games of ﬁxed games of survival Hamilton-Jacobi equation Hence hold and let inequality inf sup inf initial condition integral interval Lemma Let the conditions linear lower 6-strategy measurable function modiﬁed n-saddle need the following nonempty obtain outcome payoff set payoﬁ payoﬂ player positive constant positive number proof of Theorem Prove Theorem pure strategy pursuit-evasion game replaced saddle point satisﬁes satisfying Section strategy F sufﬁciently small suﬂiciently small Suppose T(xo terminal set trajectory corresponding uniformly Lipschitz continuous upper 6-strategy