Study of controllability of nonlinear nonautonomous dynamic systems (Q1821726)

Controllability of nonlinear nonautonomous multidimensional continuous dynamical systems is studied. A method is developed that, in many cases, makes it possible to reduce the problem of controllability for multidimensional systems to a corresponding problem for systems of smaller dimension. Several necessary and sufficient conditions for global and local controllability are obtained by this method for a certain class of dynamical systems. In particular, it is shown that the well-known algebraic conditions for controllability of nonlinear nonautonomous dynamical systems can be regarded as a consequence of the conditions given in the paper. The aim of the paper is to extend to the nonautonomous case the results presented for the autonomous case by the author [Avtom. Telemekh. 1984, No.4, 60-71 (1984; Zbl 0559.93011); English transl. in Autom. Remote Control 45, No.4, 463-472 (1984)].