Controllability with capture

A system is assumed to be governed by a set of ordinary first-order differential equations subject to control. Conditions are developed for the determination of the set of points in state space from which there exist suitable controls that can transfer these points to a single prescribed target set in a finite time interval and maintain the system within the target for all future time. A candidate for a capturing subtarget, to be used in conjunction with sufficient conditions derived here, may be obtained from conditions shown to be necessary on the boundary of the subtarget. The concepts are illustrated by an example which suggests a method of how to satisfy the sufficient conditions numerically