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The purpose of this paper is to extend the notion of regional controllability for hyperbolic parameter dependent systems.The key idea is the characterization of the averaged regional control with minimal energy.This control steers the state average (with respect to such a parameter) towards the desired state only on a given part of the system evolution domain.In this paper,we give the precis definition and the properties of this new concept.Then,we use an approach based on an extension of the Hilbert uniqueness method devoted to the calculation of the control in two different cases: zone control and pointwise control.