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Dry Clutch is one of the main components of both conventional and advanced automotive powertrain systems. Dry Clutch Control has a key role in ride comfort during standing-start and gear-shifting maneuvers. Vehicle shift performance and powertrain torque interruption are of key interest to the control problem. A faster shift time results in a more responsive vehicle but at the same time induces high level of powertrain torque interruption and vise versa. This is due to the high nonlinear behavior of the slip dependent friction torque of the vehicle's dry clutch. In this paper a dual mode control strategy for the dry clutch-by-wire system is proposed. The nonlinear behavior of the clutch friction torque is classified into two regions, a nonlinear region at a low level of clutch slip and a linear region at a high level of clutch slip. The presented control strategy switches between adaptive proportional control in the linear region and sliding mode control in the nonlinear one.