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Virtual coupling is expected to primarily improve the capacity of a railway system. Virtual coupled systems are affected by multi-source disturbances due to the complex operating environment. However, existing research only partially considers the effects of structural or external disturbances, which limits the stability and robustness of the virtually coupled train set (VCTS). In this paper, we aim to tackle the challenges arising from both structural and external disturbances in virtual coupling. We specifically propose a distributed robust model predictive control (DRMPC) solution based on a linearized model by joining linear feedback and feedforward control into a model predictive control (MPC) framework with a discrete Kalman filter (DKF). We also theoretically derive and prove a set of sufficient conditions for both local and string stabilities under structural uncertainty. The stability conditions are incorporated into the constraint space of the distributed MPC framework in order to guarantee system stability in the presence of structural and external uncertainties. The simulation results validate that our proposed control method can stabilize train platooning under both structural and external disturbances. Our control method particularly reduces the spacing and velocity tracking errors by approximately 97.55% and 99.97% on average, respectively, as compared to several baselines.
Li et al. (Thu,) studied this question.