On some constructions of control by systems with a varying structure

The method of programmed iterations in abstract control problems

“…At the same time, representation (2.12) also implies the following property: if a multifunction ~0 • M(f2, Z) exists for which (DOM)[~ °] = ~, and in addition the condition of membership in the image of the set (2.13) under the action of every operator FAsatisfied, then Q ~e O; when that happens, ~ e Q. In connection with analogues of this approach associated with the transformation S o of (2.13), we mention certain relations obtained in[29,30].3. THE METHOD OF ITERATIONS0 Representation (2.12) indicates an approach to the definition of a multiftmction in N and, in particular, 0 to the definition of (na)[~ ]; the latter multifunction contains exhaustive information about the possibility of solving the basic problem in the class of quasistrategies (see Theorem 1).…”