This paper investigates the vehicle platoon control problems with the Markov-chain switching topologies. While considering the vehicle's nonlinear dynamics and optimal energy consumption object, we propose a distributed observation based vehicle platoon control scheme. Since the switching topologies would seriously affect the effectiveness and stability of the platoon control system, we use the information of neighbor vehicles to approximate the states of the leader vehicle. In this way, it would effectively avoid the interference caused by the switching topologies. Then, for the energy consumption optimization, an energy-optimal framework of vehicle platoon is developed based on the exponential discount function. Moreover, we employ the Riccati equation to solve this optimization problem. On this basis, the stability of the proposed platoon control system is theoretically proved by constructing the Lyapunov function with the Markov-chain switching topologies. In details, as long as each possible topology contains a directed spanning tree with the root at leader vehicle, the system satisfies internal stability and input-to-state string stability(ISSS). Finally, the theoretical results are verified by numerical simulations.