Methods and a system for a vehicle control system using a reference time profile including an upper control bound and a lower control bound are provided. The system includes an input device configured to receive a required time of arrival at a waypoint and a processor communicatively coupled to said input device wherein the processor is programmed to generate a reference time profile using a first speed profile up to an intermediate control point and a second speed profile between the intermediate control point and an RTA waypoint. The system also includes an output device communicatively coupled to the processor wherein the output device is configured to transmit a speed control signal based on the reference time profile to a vehicle speed control system.