A sufficient condition for null controllability of nonlinear control systems

Classical control methods such as Pontryagin Maximum Principle and Bang-Bang Principle and other methods are not usually useful for solving {\it optimal control systems} (OCS) specially {\it optimal control of nonlinear systems} (OCNS).In this paper, we introduce a new approach for solving OCNS by using some combination of atomic measures. We define a criterion for controllability of lumped nonlinear control systems and when the system is nearly null controllable, we determine controls and states. Finally we use this criterion to solve some numerical examples.