Open AccessSufficient Conditions for Evasion in a Linear Differential Game
Author(s) -
Nodir Umrzakov,
Gafurjan Ibragimov
Publication year - 2011
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v3n4p168
Subject(s) - pursuer , mathematics , differential game , evasion (ethics) , differential (mechanical device) , pursuit evasion , set (abstract data type) , example of a game without a value , mathematical economics , repeated game , game theory , mathematical optimization , combinatorial game theory , computer science , immune system , engineering , immunology , biology , programming language , aerospace engineering
We study a linear evasion differential game in R^2. Control sets of players, the pursuer and the evader, are compact subsets of R^2. The terminal set of the game is the origin. The game is considered to be completed if the state of the system, z(t), reaches the origin. If z(t) never reaches the origin, then we say that evasion is possible in the game. We obtained weaker conditions for evasion than conditions obtained by other researches. We give some illustrative examples which show the advantage of our conditions