Distributed Model Predictive Control Strategy for Constrained High-Speed Virtually Coupled Train Set

Abstract

Virtual Coupling (VC) is regarded as a breakthrough to the traditional train operation and control for improving the capability and flexibility in railways. It brings benefits as trains under VC are allowed to operate much closer to one another, forming a virtually coupled train set (VCTS). However, the safe and stable spacing between trains in the VCTS is a problem since there are no rigid couplers to connect them into a fixed formation, especially in high-speed scenarios. Due to the close spacing, the interference between trains becomes non-negligible as various maneuvers of the preceding train can significantly affect driving behaviors of the following train; this results in fluctuating spacing and therefore an unstable VCTS. Aiming at minimizing the interference and maintaining constantly safe spacing between trains in the VCTS, this paper presents a distributed model predictive control (DMPC) approach for solving the high-speed VCTS control problem. Particularly, the proposed control method focuses on the feasibility and stability of this problem, with considerations of the coupled constraint of safety braking distance and the individual constraints of speed limit variations and restricted traction/braking performance. To guarantee feasibility and stability, the terminal controller and invariant set of the DMPC are designed. For rigor, sufficient conditions of feasibility and stability are mathematically proved and derived. Based on the data of the Beijing-Shanghai highspeed railway line, numerical experiments are conducted to verify the correctness of derived sufficient conditions and the effectiveness of the proposed control method under interference and disturbances.

Control strategy for stable formation of high‐speed virtually coupled trains with disturbances and delays

“…It is not possible to investigate the string stability of the controller in Equation ( 18) further because the controller is implicit as described in Liu et al (2022). Inspired by Zhou et al ( 2019), given that some disturbances are small and infrequent where constraints are not violated, the control problem in Equation ( 17) can be approximated by an ELQR problem: To derive the optimal control law of the ELQR in Equation (38), the batch solution is adopted (Gutierrez Soto & Adeli, 2017) 39) are directly related to the weight coefficients of the objective functions in Equations ( 17) and ( 38).…”

A Survey on Control Methods for Virtual Coupling in Railway Operation

“…However, all trains will eventually adjust to the desired state automatically, proving this method's effectiveness. Liu [35] also considered the constraints caused by the change of speed limit and traction and braking performance, proposed a distributed model predictive control (DMPC) method to ensure the stability of virtual formation, and modeled the constrained optimal control problem in the DMPC framework. Numerical simulation results show that the proposed control algorithm can maintain local stability and string stability under different initial disturbances and speed limits.…”

“…Able to improve the capability [7], [30] Able to maintain safe operation [31], [32] Suitable for analyzing the stability [33], [34], [35], [36] Suitable for modeling nonlinear optimization control problems [37], [38], [39] D: Computational Intelligent Method Suitable for scenarios where multiple trains converge to form a formation [42] Has the potential to be used in this area…”

Control predictivo por modelo robusto y descentralizado para acoplamiento virtual de trenes

“…Para cerrar el bucle, se aplica el primer input al sistema (4) durante el intervalo de tiempo [𝑡, 𝑡 + 1). 𝑢 = 𝑢 | * (11) Y en el siguiente paso de tiempo t+1, se resolverá un nuevo problema óptimo en la forma de (7 -8), basado en una nueva medición del estado, sobre un horizonte desplazado.…”

“…Esta referencia también incluye los posibles retrasos de comunicación entre el tren y el equipo de tierra RBC como parte de su estrategia de control. Asimismo, [11] desarrolla un MPC nominal distribuido para trenes de alta velocidad, evalúa su estabilidad y deriva condiciones suficientes de viabilidad y estabilidad para un pelotón de hasta dos trenes, como en [12]. Por su parte, [13] y [14] aplican un MPC nominal en metros.…”