The distributed optimal design of high-speed train movement is systematically investigated in this article. A distributed optimal control law is proposed, addressing the train consist of cars coupled by spring buffers, and is affected by aerodynamic drag and rolling resistance. A new distributed controller is proposed to decouple the train model by fully removing the in-train force, which greatly simplifies the complexity of calculation. Then the pending problem is redescribed to the control of cars with different mass. Grounded on the Lyapunov stability theory and optimal control theory, distributed optimal control law is proposed in line with guaranteed cost function, which enables faster updates of the real-time status of each car and adaptive vehicle mass. It ensures consistency in the tracking process of each car of the train, and further reduces the in-train force among cars. To eliminate the speed overshoot which results from the influence of acceleration change during train operation, we weigh in with the feed-forward compensator to assure the train's good acceleration performance. Ultimately, numerical simulations results are obtained to demonstrate convincingly the significance of our proposed control law.
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