On open-loop and feedback attainability of a closed set for nonlinear control systems
The attainability of a closed set with respect to the trajectories of a differential inclusion is studied under suitable assumptions. This property is closely related to the continuity of the minimal time function. The main result is a sufficient attainability condition. If the set is more regular, then the existence of continuous selections of the right-hand side of the differential inclusion providing the attainability property is proved. Following the main idea of [\textit{V. Veliov}, Set-Valued Anal. 5, 73-88 (1997; Zbl 0878.93054)], the set of all viable trajectories is also described.
scientific article; zbMATH DE number 1797520