To solve some control problems of nonlinear systems

A nonlinear controlled system in a finite-dimensional Euclidean space is considered. Some control tasks are formulated for it. An approach to solving problems based on the use of reachability sets and integral funnels of controlled systems and corresponding differential inclusions is discussed. Due to the complexity of the control tasks under consideration, an analytical representation of solutions for non-trivial controlled systems is impossible, and therefore this paper focuses on the issues of approximate design of solutions to problems. These issues are primarily related to the approximate construction of reachability sets and integral funnels of controlled systems. The paper also examines the problems of optimal performance of some nonlinear controlled systems, in particular, problems with phase constraints. The paper provides examples.