Control apparatus and method for automatic transmission

A dynamic model is used which shows the behavior of an automatic transmission (12) over time (t) from the start of an inertia phase. This dynamic model includes a linear term for time (t) that has elapsed and a term obtained by integrating an amount of change in a torque transmission capacity of a clutch inside the automatic transmission (12) and an amount of change in the engine torque. This dynamic model is used to estimate the input shaft rotational speed at the point at which the target inertia phase time (tir) has elapsed and start the torque-restore control at the point when it has been determined that the input shaft rotational speed Ét(tir) substantially matches a shift-end synchronous speed (Ét_af). Accordingly, it is easy to obtain preferable synchronization at the point at which the shift ends. A map need not be created to implement this control.