A vehicle powertrain includes an engine, transmission, torque converter assembly, and controller. The controller includes recorded lumped inertia models of the powertrain and instructions for executing a clutch-to-clutch shift using these models. The models collectively reduce powertrain dynamics to two or three degrees of freedom. The controller executes a method to estimate clutch torques using the models. The models may include a first primary inertia block describing engine inertia and inertia of a torque converter pump, and a second primary inertia model describing the inertia of the turbine and transmission as reflected to the input member. The second primary inertia model includes bulk inertia models for each fixed gear state and each possible shift maneuver. The controller derives a required output torque value as a closed-loop target value using the lumped inertia models and a requested input torque, and uses the estimated clutch torque to achieve the target value.