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An automatic transmission without a one-way clutch for a small sized, light weight automatic transmission is presented. The factor of torque fluctuation occurrence during shifting of the transmission increases so that the shifting is executed by controlling two wet clutches electronically in place of the one-way clutch and the wet clutch. Therefore, it is necessary to develop a new smooth gear shift control technology for clutch-to-clutch shifting on an automatic transmission without a one-way clutch. The control technology has desirable clutch-to-clutch shift control, learning control and robust control which apply to accurate signals obtained by an observation method. Smooth shifts during clutch-to-clutch shifting can be realized by recognizing clutch change-over time using a calculated acceleration and an input/output speed ratio of the transmission.