The present invention provides a control system for a dual clutch automatic transmission having a torque converter. The transmission provides seven forward speeds or gear ratios and reverse. The control system includes a hydraulic pump, a pressure regulator assembly and control valves that provide and release pressurized hydraulic fluid to the torque converter, a pair of input clutches and eight synchronizer clutches. A first pair of control valves are high flow rate valves which are capable of rapidly engaging and disengaging the input clutches. A second pair of high flow rate valves, control valves and spool valves provide a branching control circuit which controls engagement and disengagement of the synchronizer clutches. A control valve linked to the shift lever blocks hydraulic fluid flow to the first pair of high flow rate valves to inhibit input clutch activation when the shift lever is in Park or Neutral.