An analytical optimal control approach for virtually coupled high-speed trains with local and string stability

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An analytical optimal control approach for virtually coupled high-speed trains with local and string stability

Liu, Yafei / Zhou, Yang / Su, Shuai / Xun, Jing / Tang, Tao

Highlights • Optimal control with the analytical solution for the virtually coupled train set (VCTS) considering varying maneuvers and disturbances. • Derivation and proof of sufficient conditions for local stability of the linear parameter-varying VCTS system. • Derivation and proof of sufficient conditions for string stability of the homogeneous and heterogenous VCTS. • Insights into the stable region of the control parameters considering different values of the discount factor.

Abstract This paper presents an analytic optimal control method for the virtually coupled train set (VCTS) in high-speed railway, aiming at maintaining consistent speed and safe spacing among trains in the VCTS. The proposed control strategy focuses on both local and string stability under variant maneuvers in the high-speed scenarios. Specifically, a state-space model is firstly formulated to describe the virtually coupled train dynamics, based on which an optimal control formulation is then constructed considering constraints of safe spacing, operation limits and train dynamic performance. To solve the proposed constrained optimal control problem, an analytical algorithm is given based on Pontryagin’s maximum principle. Further, local and string stability are analyzed, and sufficient conditions of stability are mathematically derived to guarantee stable control for both homogeneous and heterogenous VCTS. Numerical simulations were conducted to verify the correctness of derived sufficient stability conditions and the effectiveness of the proposed control strategy under variant maneuvers and disturbances.