Extension of control problems in the class of finitely additive vector measures
Linear, continuous-time, finite-dimensional, nonstationary control systems are considered. It is generally assumed that the control constraints are of integral type. The notion of attainable set is introduced and various asymptotic properties of the attainable sets are investigated in relation to the perturbations of the integral constraints. In the proofs, finitely additive vector measure methods are used. Moreover, several remarks and comments concerning the properties of the attainable sets and related optimal control problems are given. Asymptotic attainability problems have been recently considered in the paper [\textit{A. G. Chentsov} and \textit{S. I. Morina}, Funct. Differ. Equ. 2, 23-37 (1994; Zbl 0874.93016)].
scientific article; zbMATH DE number 1263172