On Some Nonlinear Control System Problems on a Finite Time Interval

In this presentation we evaluate nonlinear control systems on a finite time interval. We also discuss application of the invariance features and weak invariant sets in the procedures of constructing solutions for approach problems. These problems are closely connected with evaluation of reachability sets and integral funnels of control systems. We revise several problems of approaching and one general scheme of constructing solutions for these problems. Scheme consist of two stages: at the first stage we construct approximate reachability set of the approach problem; at the second stage in one way or another we construct control on a given time interval that solves the approach problem. © 201