On near-controllability of nonlinear control systems

In this paper, the notion of near-controllability is established for nonlinear systems. This notion includes the general notion of controllability. It is shown that, by presenting nearly controllable examples including the continuous-time case and the discrete-time case, the property of near-controllability exists widely in nonlinear systems. Therefore, near-controllability is a fundamental property of nonlinear systems. Furthermore, near-controllability can better characterize the properties of control systems than controllability, as shown in the examples that are uncontrollable but nearly controllable.