It usually takes a long time to obtain a target orbit by controlling chaos. But a chaotic system sometimes cannot be effectively controlled , which is shown in the feedback control based on forecasting. Among the reasons , one is that chaotic models may have many fixed points , the other is the density of orbits. In order to know when to control , an equivalence relation is introduced in this paper. The characteristic exponent based on a probabilistic dy2 namical system is calculated , which provides some useful information on unstable periodic orbits of the chaotic eco2 nomic dynamical system. An effective controlling parameter is chosen by discussing the sign of the characteristic ex2 ponent . Furthermore , the control regions of the parameter variable are proposed. Therefore the controllable domain of chaos in the chaotic economic model can be obtained.