A vehicle includes an engine, a dry dual-clutch transmission (dDCT) having a pair of input clutches and a gearbox containing oddly- and evenly-numbered gear sets, and a transmission control module (TCM). Application of one of input clutches connects the engine to a corresponding one of the oddly- or evenly-numbered gear sets. The TCM includes feed-forward PID-based control logic, and a torque-to-position (TTP) table for each input clutch. The TCM commands a position of a designated input clutch during a power-on upshift using the feed-forward, PID-based control logic, and selectively adapts the TTP table as a function of an inertia and acceleration value of the engine. The TCM may apply an asymmetrical handoff profile to commanded oncoming and offgoing clutch torques during the torque phase of the upshift. The TCM may also adjust the TTP table as a function of the frequency of use of the input clutches.