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This book addresses the issue of road congestion due to increased traffic in urban and metropolitan areas and the design of an autonomous longitudinal speed controller as a solution to this problem. One of the best ways to increase efficiency of the available road infrastructure is to enable vehicles to move in a platoon with very small distance headway from the preceding vehicle. A Longitudinal Finite State Machine has been developed which acts as a supervisory control to help the following vehicle to merge behind and follow the preceding vehicle. This book also presents the study of the performance of two vehicle following controllers, i.e. LQR based full-state feedback controller and LQR based sequential-state feedback controller, which are enabled and take the control of the vehicle velocity during the follow state of the vehicle s Longitudinal FSM. Finally, a comparison analysis has been presented between the two controllers which help in reducing the distance headway from the preceding vehicle as well as maintaining string stability within the platoon.