Time limits in the control of pollution systems

Exponentially growing pollution systems are examined from the point of view of control. A simplified mathematical model is used. Employing optimal control theory, we show that it is not always possible to drive the state (level of pollution) of such a system to a desired level. We prove that the state has to be smaller than certain bound for the system to be controllable. A specific example illustrates these ideas. The importance of this research lies in the fact that it shows the existence of certain state, and, consequently, time limits in the process of controlling the system.