Tereshchenko I. The problems of pursuit-evasion and deduction in differential and deduction games

Thesis is devoted to games of pursuit-evasion and deduction in continuous and discreet positions. The sets of different initial positions favorable to this or that player have been constructed. The structure of the game in general case is described by B.M. Pshenychniy's operator constructions. With the help of the H-convex sets method linear differential game of dynamic system trajectory deduction in terminal set on additional half axis is solved in new problem statement. The conditions "of a complete sweeping" that was used while solving the discreet problem of deduction that allowed to build minimum and maximum invariant sets. The results of invariant sets building in discreet problem were transferred on continuous problem case. For linear differential games of pursuit-evasion with fixed finishing time new methods of these games solutions were developed, in these case, the main role of condition "of a complete sweeping" plays in these methods. At the basis "of a complete sweeping" new problems of pursuit-evasion with fixed finishing time and with terminal set of condition were solved. Formulas that estimate the value of the game were obtained.