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This paper considers using linear quadratic regulation (LQR) for multi-input control of the Automatic Transmission (AT) upshift inertia phase. The considered control inputs include the transmission input/engine torque, oncoming clutch torque, and traditionally not used off-going clutch torque. Use of the off-going clutch has been motivated by discussed Control Trajectory Optimization (CTO) results demonstrating that employing the off-going clutch during the inertia phase along with the main, oncoming clutch can improve the upshift control performance in terms of the shift duration and/or comfort by trading off the transmission efficiency and control simplicity to some extent. The proposed LQR approach provides setting an optimal trade-off between the conflicting criteria related to driving comfort and clutches thermal energy loss.