The emerging virtual coupling technology aims to connect multiple train units as a virtually coupled train set (VCTS) with outstanding operation efficiency and flexibility. This paper studies the nonlinear formation control of VCTS, particularly considering the uncertainties from external disturbances and the practical modeling of formations. To solve this problem, we propose a distributed robust nonlinear model predictive control approach using tube techniques. Based on the analysis of contractiveness, nonlinear tubes are constructed to confine the uncertain trajectory influenced by uncertainties from the formation model, disturbances and distributed prediction. Specifically, to facilitate tube construction, compatibility constraints are deployed to restrict uncertainties from distributed prediction. Furthermore, the robust constraint satisfaction, recursive feasibility and stability of VCTS operations are established. Finally, based on the practical data in field tests, comparative experiments are conducted to demonstrate the advantages of our approach in control performance and computational efficiency.

Reducing system energy consumption and passenger waiting time is essential for enhancing the efficiency of urban rail transit systems. Current research on train scheduling based on reinforcement learning typically merges these two objectives into a single metric, producing only one optimal solution. This paper proposes a multi-objective multi-agent reinforcement learning method for train scheduling that comprehensively considers the two goals and generates multiple non-dominated solutions. The decision variables include dispatching times, train formations, and inter-station running times for the entire day. Compared to the genetic algorithm and an existing multi-objective reinforce-ment learning algorithm, our method achieves a more efficient Pareto front with reduced training time. The effectiveness of the method is demonstrated through a numerical example using de-sensitized data from the Chongqing Metro, effectively balancing energy savings with the quality of passenger services.

This paper studies a minimal-energy driving strategy for high-speed electric trains with a fixed travel time. A hybrid system model is proposed to describe the new characteristics of high-speed electric trains, including the extended speed range, energy efficiency, and regenerative braking. Based on this model, train driving is characterized by the gear sequence and the switching locations. An approximate gradient information is derived via the variational principle. To avoid a combinatorial explosion, the gear sequence is fixed by a priori knowledge. Then, a gradient-based exterior point method is proposed to calculate the optimal driving. In the case study, the minimal-energy driving with a fixed travel time for CRH-3 is investigated, and the result reveals some new understandings for high-speed electric train drive. Additionally, the tradeoff relationship between energy consumption and travel time is quantitatively studied, which is helpful in assigning an appropriate travel time for high-speed trains.

In this paper, we are concerned with the H∞model reduction problem for a class of nonlinear time-varying systems with parameter uncertainties and time delays in a discrete time framework. By introducing a proper Lyapunov function, we establish a sufficient condition ensuring the asymptotically mean square stability of the associate error system with a prescribed H∞error performance in the form of quasi-linear matrix inequality, based on which the parameters of the reduced-order model can also be determined. Finally, a numerical example is included to show the effectiveness of the developed technique.

While a specific system is in use, its reliability will decrease gradually after the infant mortality period because of the components' degradation, or external attacks. Thus, reliability is a natural characteristic of a system's health, and can be used for condition monitoring & predictive maintenance. This paper introduces a new real-time reliability prediction method for dynamic systems which incorporates an on-line fault prediction algorithm. The factors that may reduce a system's reliability are modeled as an additive fault input to the system, and the fault is assumed to be varying linearly with time, approximately. The time-varying fault is roughly estimated based on a modified particle filtering algorithm at first. Then, as a time series, the fault estimate sequence is smoothed, and predicted by an exponential smoothing method. Mathematical analysis shows that the effects of the system, and measurement noises on the fault estimates are greatly reduced by exponential smoothing, which indicates that the comparatively high accuracy of the fault estimates & predictions is guaranteed. Based on the particle filtering & fault prediction results, the whole system's predictive reliability is computed through a Monte Carlo simulation strategy. The effectiveness of the proposed real-time reliability prediction method is validated by a computer simulation of a three-vessel water tank system.

This paper introduces a real-time reliability prediction method for a dynamic system which suffers from a hidden degradation process. The hidden degradation process is firstly identified by use of particle filtering based on measurable outputs of the considered dynamic system. Then the system's reliability is predicted according to the model of the degradation path. We analyze the identification algorithm mathematically, and validate the effectiveness of this method through computer simulations of a three-vessel water tank. This real-time reliability prediction method is beneficial to the dynamic system's condition monitoring, and may be further helpful to make a proper predictive maintenance policy for the system.

As an uncertainty data analysis method, rough set theory can be used to retrieve classification rules from the given data by partitioning the data according to the indiscernibility relations. The evaluation of uncertainty of rough classification rules needs some proper uncertainty measures. The uncertainty coming from the granularity of the partition includes inconsistency and randomness. Unlike the approximation quality of rough sets, the information entropy based uncertainty measures can deal with the two aspects of uncertainty. On the other hand, the noise in the given data can make the inconsistency overestimated. As a result, some originally consistent rules may become inconsistent and be rejected improperly. Inspired by variable precision rough set model, we construct two new uncertainty measures, which have some tolerance for the inconsistency of the data. Experimental results illustrate the fitness of them to evaluate the classification rules retrieved from the noisy data.