Asymptotic attainability in the abstract control problem unter perturbed integral constraints. II (Q1909816)

Asymptotic properties of the attainable sets for finite-dimensional continuous-time control systems are considered. Using topological methods and finitely-additive measures, asymptotic inertness of an attainable set is investigated when some of the control constraints are perturbed. It is generally assumed that the perturbations are integrally constrained. The asymptotic inertness conditions stated in the paper determine in particular, some kinds of stability for an attainable set. Moreover, several remarks and comments on the behaviours of the attainable sets for linear control systems are presented. Similar considerations can be found in the paper, [\textit{A. G. Chentsov}, Kibernetika 1990, No. 6, 78-84 (1990; Zbl 0748.49030)].