In deep waters scenarios Tension Leg Platforms, under severe sea/wind conditions, may experience large response amplitudes of the hull motion. Large heave amplitudes caused by dynamic loads appear as one of the most deleterious effects to the structural safety and integrity of the mooring system and the hanging risers. This paper shows that active/passive control systems may be installed inside the hull to attenuate dynamic amplitudes in heave motion of such floating structures. Energy absorption techniques and optimal control theory are applied to allow for the idealization of a mechanism to reduce the dynamic response amplitude to required values, improving safety conditions and increasing service life of tendons and risers, insuring the system functionality and reliability at all.