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This paper puts forward the robust control problem of rail vehicle virtual coupling platoon that is subject to nonlinear and time-varying uncertainties. The uncertainties are caused by external disturbances and parameter variations. To this end, this paper designs a robust controller based on the Udwadia-Kalaba (UK) equation. First, we introduce the concept of virtual coupling and establish the longitudinal dynamics model of the rail vehicle. In order to ensure the control objective of the virtual coupling process, the spatial constraint on position and bidirectional inequality constraints for the spacing error between the marshalling trains are established. After changing the bounded state into the unbounded state through the state transformation, the UK approach can be used. Then, the constraint-following robust controller design is based on the UK approach and Lyapunov stability theory. The controller can render the unbounded state eventual uniform boundedness and uniformultimate boundedness, which also satisfies the spatial constraint and the bidirectional restriction for the spacing error. Moreover, an optimized design scheme for the tunable parameter of this controller is proposed, which minimizes the control cost and comprehensive index of system performance. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]