A control apparatus mounted on a vehicle including, on a path for transmitting a torque output from an engine, a clutch of which torque capacity changes in accordance with an operation of an actuator, and a dog clutch transmission mechanism mounted downstream of the clutch, the control apparatus being programmed to execute rotation control for changing a rotation speed of the engine in a gear change period by giving an instruction value to the actuator such that the torque capacity of the clutch becomes greater or smaller relative to the torque output from the engine, the control apparatus comprising: a holding unit for holding condition-specific information a relationship between the torque capacity and the instruction value to be given to the actuator; a deciding unit for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity; and a control unit for changing the rotation speed of the engine by giving the decided instruction value to the actuator, characterized in that the holding unit is configured for holding condition-specific information by a plurality of tables indicating a relationship between the torque capacity and the instruction value to be given to the actuator, for being applied under each of a plurality of driving conditions that lead to different torque capacities generated in the clutch despite a same instruction value is given to the actuator or a plurality of driving conditions that lead to different characteristics in change of the rotation speed of the engine despite a same torque capacity is generated in the clutch; a determining unit is provided for determining under which driving condition among the plurality of driving conditions a gear change is executed; and the deciding unit is configured for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity, based on a table of the plurality of tables, the table is applied under the determined driving condition. the control apparatus being programmed to execute rotation control for changing a rotation speed of the engine in a gear change period by giving an instruction value to the actuator such that the torque capacity of the clutch becomes greater or smaller relative to the torque output from the engine, the control apparatus comprising: a holding unit for holding condition-specific information a relationship between the torque capacity and the instruction value to be given to the actuator; a deciding unit for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity; and a control unit for changing the rotation speed of the engine by giving the decided instruction value to the actuator, characterized in that the holding unit is configured for holding condition-specific information by a plurality of tables indicating a relationship between the torque capacity and the instruction value to be given to the actuator, for being applied under each of a plurality of driving conditions that lead to different torque capacities generated in the clutch despite a same instruction value is given to the actuator or a plurality of driving conditions that lead to different characteristics in change of the rotation speed of the engine despite a same torque capacity is generated in the clutch; a determining unit is provided for determining under which driving condition among the plurality of driving conditions a gear change is executed; and the deciding unit is configured for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity, based on a table of the plurality of tables, the table is applied under the determined driving condition. a holding unit for holding condition-specific information a relationship between the torque capacity and the instruction value to be given to the actuator; a deciding unit for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity; and a control unit for changing the rotation speed of the engine by giving the decided instruction value to the actuator, characterized in that the holding unit is configured for holding condition-specific information by a plurality of tables indicating a relationship between the torque capacity and the instruction value to be given to the actuator, for being applied under each of a plurality of driving conditions that lead to different torque capacities generated in the clutch despite a same instruction value is given to the actuator or a plurality of driving conditions that lead to different characteristics in change of the rotation speed of the engine despite a same torque capacity is generated in the clutch; a determining unit is provided for determining under which driving condition among the plurality of driving conditions a gear change is executed; and the deciding unit is configured for deciding an instruction value to be given to the actuator corresponding to a target value of the torque capacity, based on a table of the plurality of tables, the table is applied under the determined driving condition.