On the question of approximate calculation of the attainability set for controllable systems with delay (Q1898583)

Nonlinear, time-invariant control systems with lumped constant delay in the state variables are considered. Using differential inclusion methods, a construction of approximations of the attainable sets in finite time is presented. Under some general assumptions, the Hausdorff distance between an attainable set and its approximation is calculated. Moreover, in the linear case some additional parameters for the attainable sets are determined. Similar problems but for control systems without delays have been investigated in the paper [\textit{M. S. Nikol'skij}, Mosc. Univ. Comput. Math. Cybern. 1987, No. 4, 33-37 (1987); translation from Vestn. Mosk. Univ., Ser. XV 1987, No. 4, 31-34 (1987; Zbl 0715.65053)].