Asymptotic attainability in the abstract control problem under perturbed integral constraints. I
Linear finite-dimensional continuous-time control systems are considered. The asymptotic behaviour of the attainable sets under perturbations of integrally constrained controls are investigated. Using topological methods and Cauchy formula for linear control systems, the asymptotic inertness property for attainable sets is derived. Moreover, generalized integral contraints and their relaxations are also discussed. Finally several remarks and comments on the properties of the attainable sets are given. Similar control problems with integral constraints can be found in the paper [\textit{V. P. Serov} and \textit{A. G. Chentsov}, Differ. Uravn. No. 4, 607-618 (1990; Zbl 0707.49002)].
scientific article; zbMATH DE number 857484