Abstract-This paper presents a longitudinal tracking control law for Cooperative Adaptive Cruise Control (CACC) systems in a platoon that can comprehensively enable tracking capability of various spacing policies, designed expected velocity, and designed expected acceleration. Taking into account heterogeneous traffic, i.e., a platoon of vehicles with possibly different characteristics, the longitudinal control problem is formulated as an output tracking control problem with a quadratic function so that the contradictions among the different tracking requirements are realized, which include inter-vehicle spacing, velocity and acceleration. Then, the decentralized longitudinal tracking control law is proposed by using a limited communication structure and maximum principle (in this case, a wireless communication link with the nearest preceding vehicle and designed platoon leader only), in which the feedback items are composed of the states of host vehicles, and additional information of the nearest preceding vehicle and designed platoon leader are used as feedforward items. In addition, the concepts of "expected velocity" and "expected acceleration" are introduced to design the desired velocity and acceleration, realize additional objectives, and improve the predictive abilities. Numerous simulation results show that the proposed tracking controller provides a reliable tool for a systematic and efficient design of a platoon controller within CACC systems.