Methods for solving a boundary value problem for nonlinear controlled systems of ordinary differential equations in the class of piecewise constant controls

Algorithms for solving local and global boundary value problems for nonlinear and quasilinear nonstationary control systems in the class of piecewise constant controls are developed. Constructive sufficient conditions are found that guarantee the existence of solutions to these problems. In addition, a Kalmantype criterion for local and global controllability of nonlinear and quasilinear stationary systems, respectively, is obtained. The performance of the algorithms is illustrated by numerical simulation of the solution to the problem of controlling the motion of a robotic manipulator.