in controlling an automatic transmission in a vehicle by a combination of an electronic computer system and a hydraulic actuation system according to a principle of feedback control so that the electronic computer system computes a target control state for the hydraulic actuation system and the hydraulic actuation system is operated according to a difference between the target control state and a current control state thereof , the difference is modified by an amount which is decreased along with lapse of time so that the delay in the operation of the hydraulic actuation system is compensated for by a simulation that at the start of control the difference is beforehand increased for an amount which is gradually cancelled by a delay function of the difference itself as the delay in the operation of the hydraulic actuation system disappears . the difference may further be modified so that the modification is started with a time lag . the difference may further be modified by the rate of change of itself .