On the Controllability of Nonlinear Control Systems

Abstract

In this paper, some discussions for the controllability in nonlinear systems are presented. At first various concepts about controllability are denned. In section 3, one dimensional systems are treated and sufficient conditions for controllability are obtained. In section 4, we discuss the controllability of nonlinear systems with controls appearing linearly and show that it is possible to reduce the controllability of the given system to that of some lower dimensional system. One result in section 3 is extended to n-dimensional system in the following section. In section 6, the concept of the controllability in the local sense is introduced according to L. Markus. At last, relations between various concepts of controllability are shown.