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Order Preserving Properties of Vehicle Dynamics with Respect to the Driver's Input

In this report, we consider longitudinal dynamics of a vehicle and prove that its longitudinal position and velocity are order preserving with respect to the driver’s (or automatic controller’s) input. We also prove that the position is strictly order preserving with respect to the constant term of the acceleration replaced with a linear function of the position and the velocity. This estimation of the acceleration is used for the cases in which no direct measurement of the acceleration is available.