On a Controllable Region of a Certain Divergent System

Abstract

In optimal control problems, it is known that not all the states of a system can be transfered to the desired final state by an admissible control. This paper presents a new method for calculating a controllable region which is defined as a set of the states that can be transfered to the desired state in a finite time by an admissible control. For this purpose, a certain function, which was originally used for computing time-optimal controls, is introduced, and the boundary of the controllable region can be obtained by evaluating the limit of this function as time t tends to infinity. As an example, a second order divergent system with complex eigenvalues is treated.