Multivalued Quasistrategies and the Method of Program Iterations

摘要

For an abstract control system admitting a combination of fragments with continuous and discrete time, we consider the game problem of approaching a given set involving nonstationary phase constraints. A new version of the known method of program iterations used earlier in the theory of differential games is constructed. In this version, the structure of a solution in the class of multivalued quasistrategies is obtained. This structure includes the construction of a set of successful solvability and a representation of the decision quasistrategies as nonsingular fixed points of a "program" operator.