Approximately nearly controllability of discrete-time bilinear control systems with control input characteristic

In this paper we study a class of discrete-time bilinear control systems that can be used to model the production storage management problems. A weaker but more applicable concept of controllability, approximately nearly controllability, is proposed under the framework of hypercyclicity from the theory of dynamical systems. The complete characteristic of the system structure for being approximately nearly controllable is provided. Necessary and sufficient conditions for the system to be approximately nearly controllable are presented. Moreover, the required number of different input values for the system to achieve the approximately nearly controllability during the evolutionary process is obtained.