Rurenko O. Linear integral and integral-differencial games of approach

New classes of conflict-controlled processes with evolution, presented by Volterra integral operators, are defined and investigated in the thesis. The class of integral games and the classes of integral-differential games with various form control blocks are treated in detail. It is shown that these games evolution in may be presented by Volterra integral operators. On the basis of the method of resolving functions sufficient conditions are obtained, which make it feasible to drive in a finite time the process trajectory to a cylindrical terminal set. Special matrix function is introduced, which is a generalization of Mittag-Leffler function. With its here the second-order systems of Volterra integral and integral-differential equations, having difference kernels and possessing polar peculiarities, are studied. On the basis of asymptotic as properties of Mittag-Leffler generalized functions, for the guaranteed approach times and the "pursuer's" counter-controls explicit formulas are derived in term s of the game parameters.