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Human hand can not only catch and grasp the complex objects but also easily manipulate the objects by switching various types of interactions. Research on the basic mechanics and control principles of hand's dexterous manipulation abilities is one of the most important subjects in bio-mimetics. In this paper, we formalize the multi-fingered hand manipulation problem as a general dynamic complementarity (DC) system. Based on the fact that the DC system can be transformed to a mixed logical dynamical (MLD) model, and that MLD system can control problem can be solved using powerful mixed integer programming (MIP) algorithm, we propose to realize dexterous hand manipulations by using a cyber-grasp system, and study its robotic realization on GIFU hand III, which is equipped with tactile sensors. We suggest that in order to obtain sub-optimal solutions, biologically inspired techniques might be very powerful.