According to some aspects, methods and systems are presented to reduce noise, vibration, and harshness during start or restart of an engine. In some embodiments, a torque source such as an electric machine provides a torque to an internal combustion engine during restart to counteract vibrations of the system caused by the output torque of the internal combustion engine. The torque provided by the torque source can be expressed as a sum of a non-linear component and an input shaped component. A perturbation technique can be utilized for separating the scales and isolating the non-linear response of the system. Command shaping can be applied to the remaining, linear response of the system. Parameters used in the modeling of the internal combustion engine and the system may be pre-determined based on vehicle design and operating conditions, or may be iteratively estimated based on previous restarts during vehicle operation.

An idle stop condition determination method of an engine includes: calculating and storing a fuel saving estimation amount in idle stop of an engine on the basis of traveling information; calculating the amount of fuel consumption in restarting for restarting, when an idle stop condition of the engine is satisfied; comparing the magnitudes of the fuel saving estimation amount with the amount of fuel consumption in restarting, and stopping the engine in accordance with the result of the comparing; and restarting the engine, when a restarting condition of the engine is satisfied.

A vehicle comprises: a storage battery configured to store electric power; an internal combustion engine configured to be started with electric power supplied from the storage battery; an electric auxiliary configured to operate with the electric power supplied from the storage battery; and a stop start controller configured to perform a stop control of stopping the internal combustion engine according to a driving condition of the vehicle and a restart control of restarting the internal combustion engine that has been stopped by the stop control. The stop start controller includes: an auxiliary voltage acquirer configured to obtain a measured auxiliary voltage value that denotes a voltage of the electric auxiliary measured on occasion of start of the internal combustion engine; and a feasibility determiner configured to determine whether the stop control is feasible, based on the measured auxiliary voltage value.