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Existence of value in a differential game

✍ Scribed by L.S. Zaremba

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
302 KB
Volume
1
Category
Article
ISSN
0167-6911

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✦ Synopsis

A two-person zero-sum differential game with general type phase constraints and the cost function of the form C = mllX{a(l.X(I). y(fΒ»: ,*,,"I.,.;T M }. where TAl denotes the end of the game. is investigated. Player I possesing incomplete informution can select any lower rI-strategy (in the Friedman sense). while player II having complete information can choose any strategy in the Varaiya-Lin sense. The existence of a vulue lind un optimal strategy for player II is proved under assumptions ensuring the set of all admissible trajectories for player II is compact in the Banach space of all continuous functions.

gives to player I an amount c:::C[x(-),YC)] = sup a(t,x(t),y(t)); I. ";'/-., Til c= fTh(t, x(t),y{t)) dt r. and ( 1.3) ( 1.4) ( 1.5) ( 1.2) ( 1.1

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