Modern railway trains raise higher demands on stability, operational efficiency, and comfort. To this end, distributed tracking control is vital to improve tracking performance and reduce the coupling force between traction units. This paper presents a novel adaptive cooperative tracking control approach for high-speed trains based on a multi-agent model. The proposed method ensures accurate tracking of both displacement and velocity, and effectively mitigates the coupling forces between adjacent traction units. Specifically, an improved multi-agent model of the high-speed train is developed, in which uncertain nonlinear resistance is approximated using an adaptive neural network, and the coupler connecting adjacent agents (traction units) is modeled as a spring-damper system. To formulate a refined controller, prior knowledge of the train system, such as the inherent resistance and coupling structure, is fully utilized so that only a few unknown parameters need to be estimated. Furthermore, an adaptive cooperative controller is designed to achieve accurate speed and displacement tracking. With this controller, multiple agents are simultaneously coordinated, while nonlinearities and uncertainties are handled. The coupling force between adjacent agents is effectively mitigated compared to traditional methods. Comparative simulation studies are conducted to demonstrate the effectiveness of the proposed adaptive cooperative tracking controller.

Distributed Kalman filtering is a widely used technique for state estimation in sensor networks system. Typically, each node utilizes the measurement residuals and the information exchanged with the neighbors to obtain the fused state estimation. However, local measurement is susceptible to outliers, and data sharing leads to privacy and security issues. In this paper, a secure and privacy-preserving distributed Kalman filter (SPP-DKF) is developed to simultaneously address the aforementioned issues. Specifically, the outlier-resistant mechanism is embedded to improve the resilience of the distributed Kalman filter, which employs the saturation function to suppress the mutation of innovation caused by outliers. An event-triggered privacy-preserving scheme based on dynamic mask is designed to protect privacy of local state against different adversaries. Meanwhile, to ensure security, the digital signature based on homomorphic encryption and hash function is adopted to detect false data injection attacks. Furthermore, the mean-square estimation performance and the upper bound of the error covariance of the proposed SPP-DKF are analyzed. In addition, the privacy and security performance of the proposed algorithm are also ensured. Finally, simulation results indicate that the proposed SPP-DKF provides reliable estimation performance while ensuring the privacy and security of the exchanged data.