The J-turn is a manoeuvre in which the driver performs a steering-wheel step input. The steady-state yaw rate is an objective function we have to consider. Y is the steady-state yaw rate that is reached when the car runs steadily after the steering-wheel step input has been introduced. As we have to minimise all of the objective functions and we want actually to have Y as high as possible we have to construct this objective function (see formula) which allows to minimise this performance index. Another objective function to be minimised is the overshoot. Also, we want to minimise the TB factor, that is the product between the angle between the centre line of the vehicle and the direction of the velocity of the centre of gravity of the vehicle and the time at which the overshoot, (the maximum yaw rate) occurs. If I minimise this I will get a vehicle which runs tangential with respect to the curve path and a vehicle which is reactive, that is a vehicle which approaches to the steady-state yaw rate as fast as possible.

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