This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.

This paper presents a nonlinear observer-based actuator fault diagnosis framework for a class of Lipschitz nonlinear systems in the presence of actuator faults, including both multiplicative and additive types. The proposed diagnosis algorithm leverages a nonlinear observer designed using a modified linear quadratic Riccati equation that ensures exponential convergence of the state estimation error, independent of the Lipschitz constant. A deterministic threshold-based detection mechanism is then developed to detect fault occurrences. The framework further distinguishes between multiplicative and additive faults by leveraging specific control strategies and dynamic analysis. Theoretical results are validated with rigorous stability proofs, ensuring robustness and fault isolation capabilities. This framework provides a systematic solution for fault detection, isolation, and diagnosis in complex nonlinear systems.

The railway timetable rescheduling problem is regarded as an efficient way to handle disturbances. Typically, it is tackled using a mixed integer linear programming (MILP) formulation. In this paper, an algorithm that combines both reinforcement learning and optimization is proposed to solve the railway timetable rescheduling problem. Specifically, a value-based reinforcement learning algorithm is implemented to determine the independent integer variables of the MILP problem. Then, the values of all the integer variables can be derived from these independent integer variables. With the solution for the integer variables, the MILP problem can be transformed into a linear programming problem, which can be solved efficiently. The simulation results show that the proposed method can reduce passenger delays compared with the baseline, while also reducing the solution time.

Virtual coupling is regarded as an efficient way to improve the line capacity of rail transportation systems by reducing the spacing between consecutive trains. This paper is the first to compare and assess different distributed model predictive control (MPC) approaches, i.e., cooperative distributed MPC, serial distributed MPC, and decentralized MPC, for virtually coupled trains with a nonlinear train dynamic model. To make a balanced trade-off between computational complexity and efficiency, we also propose and assess convex approximations of the above control approaches. Furthermore, we are the first to introduce the relaxed dynamic programming approach to analyze the stability of the MPC-based nonlinear train control problem. By using the relaxed dynamic programming approach, a distributed stopping criterion with a stability guarantee is developed for the cooperative distributed MPC approach. In real life, masses of trains are different and can change at stations due to changes in passenger loads. This change in mass can significantly affect the dynamics and control of the virtually coupled trains when not taken into account in the control design. Therefore, we explicitly consider heterogeneous train masses when designing MPC approaches. We evaluate the different distributed MPC approaches through case studies based on the data of the Beijing Yizhuang Line. Simulation results indicate that the cooperative distributed MPC approach has the best tracking performance, while the serial distributed MPC approach can reduce communication requirements and computation capabilities with sacrifices of tracking performance.

Real-time train scheduling is essential for passenger satisfaction in urban rail transit networks. This paper focuses on real-time train scheduling for urban rail transit networks considering uncertain time-dependent passenger origin-destination demands. First, a macroscopic passenger flow model we proposed before is extended to include rolling stock availability. Then, a distributed-knowledgeable-reduced-horizon (DKRH) algorithm is developed to deal with the computational burden and the communication restrictions of the train scheduling problem in urban rail transit networks. For the DKRH algorithm, a cost-to-go function is designed to reduce the prediction horizon of the original model predictive control approach while taking into account the control performance. By applying a scenario reduction approach, a scenario-based distributed-knowledgeable-reduced-horizon (S-DKRH) algorithm is proposed to handle the uncertain passenger flows with an acceptable increase in computation time. Numerical experiments are conducted to evaluate the effectiveness of the developed DKRH and S-DKRH algorithms based on real-life data from the Beijing urban rail transit network. The simulation results indicate that DKRH can be used to achieve real-time train scheduling for the urban rail transit network, while S-DKRH can handle the uncertainty in the passenger flows with an acceptable sacrifice in computation time.

The integration of autonomous vehicles and on-demand customized bus systems is expected to be beneficial for responding to real-time demands. This paper investigates the autonomous customized bus (ACB) system that leverages passenger demand prediction to enhance service quality and vehicle utilization. A novel ACB service design optimization model that determines vehicle movements and passenger-to-vehicle assignments is developed for the real-time routing and scheduling problem. Then, a rolling horizon approach, incorporating travel demand prediction, proactive dispatching and reactive adjustment, is proposed to address the studied problem. The performance of the introduced ACB system is evaluated using smartcard data from Beijing and the state-of-the-art machine learning algorithm. Results show that the proposed ACB system can effectively improve system performance and service level in terms of operating cost and passenger waiting time compared to reactive operations.

Timetables determine the service quality for passengers and the energy consumption of trains in metro systems. In metro networks, a timetable can be made by designing train departure frequencies for different periods of the day, which is typically formulated as a mixed-integer linear programming (MILP) problem. In this paper, we first apply Benders decomposition to optimize the departure frequencies considering time-varying passenger origin-destination demands in metro networks. An ϵ -optimal Benders decomposition approach is subsequently used to reduce the solution time further. The performance of both methods is illustrated in a simulation-based case study using a grid metro network. The results show that both the classical Benders decomposition approach and the ϵ -optimal Benders decomposition approach can significantly reduce the computation time for the optimization of train departure frequencies in metro networks. In addition, the ϵ -optimal Benders decomposition approach can further reduce the solution time compared to the classical Benders decomposition approach when the problem scale increases while maintaining an acceptable level of performance.

This paper deals with the train scheduling problem for metro networks taking into account time-dependent passenger origin–destination demands and train speed profiles. The aim is to adjust train schedules online according to time-dependent passenger demands so that passenger satisfaction and operational costs are jointly optimized. An extended passenger absorption model that explicitly includes time-dependent passenger origin–destination demands is developed, where the term “absorption” refers to passengers boarding trains. Then, the passenger absorption model is extended to a bi-level framework, where passenger demands and rolling stock availability are considered at the higher level, and detailed timetables and train speed profiles are included at the lower level. A bi-level model predictive control (MPC) approach is developed for the integrated problem. The optimization problems of both levels of the bi-level MPC approach can be converted into mixed-integer linear programming (MILP) problems, which enables us to solve them with existing MILP solvers. We then show that the recursive feasibility of both the higher-level and the lower-level optimization problems can be guaranteed. In this way, we can achieve real-time train scheduling for the metro system. Numerical experiments, based on real-life data from the Beijing metro network, illustrate the effectiveness of the extended passenger absorption model and the proposed bi-level MPC approach.

Effective timetable scheduling strategies are essential for passenger satisfaction in urban rail transit networks. Most existing passenger-centric timetable scheduling approaches generate a timetable according to deterministic passenger origin-destination (OD) demands. As passenger OD demands in urban rail transit networks generally show a high level of uncertainty, an effective timetable scheduling approach should take the uncertain passenger flows into account to generate a reliable timetable. In this paper, a scenario-based model predictive control (SMPC) approach is presented to handle uncertain passenger flows based on a passenger absorption model, where uncertainties are captured by several representative scenarios according to historical data. In each SMPC step, the optimization problem for generating the timetable can be reformulated as a mixed-integer linear programming (MILP) problem, which can be efficiently solved using current MILP solvers. A probabilistic performance level can be then determined based on the performance of SMPC under the representative scenarios. Numerical experiments based on the Beijing subway network are conducted to evaluate the efficacy of the proposed approach.

Real-time timetable scheduling is an effective way to improve passenger satisfaction and to reduce operational costs in urban rail transit networks. In this paper, a novel passenger-oriented network model is developed for real-time timetable scheduling that can model time-dependent passenger origin-destination demands with consideration of a balanced trade-off between model accuracy and computation speed. Then, a model predictive control (MPC) approach is proposed for the timetable scheduling problem based on the developed model. The resulting MPC optimization problem is a nonlinear non-convex problem. In this context, the online computational complexity becomes the main issue for the real-time feasibility of MPC. To reduce the online computational complexity, the MPC optimization problem is therefore reformulated into a mixed-integer linear programming (MILP) problem. The resulting MILP problem is exactly equivalent to the original MPC optimization problem and can be solved very efficiently by existing MILP solvers, so that we can obtain the solution very fast and realize real-time timetable scheduling. Numerical experiments based on a part of Beijing subway network show the effectiveness and efficiency of the developed model and the MILP-based MPC method.

Timetable scheduling plays a key role in daily operations of urban rail transit systems, as it determines the quality of service provided to passengers. In order to develop efficient timetable scheduling methods, it is necessary to develop a proper model to integrate timetable-related and passenger-related factors in urban rail network efficiently. In this paper, a novel passenger absorption model for passenger- centric urban rail networks is established. The model explicitly integrates time-varying passenger origin-destination demands and the departure frequency of each line for real-time timetable scheduling. Then, a model predictive control (MPC) method for the timetable scheduling problem is proposed based on the developed model. The resulting MPC optimization problem can be formulated as a mixed-integer programming (MILP) problem, which can be solved efficiently by using the existing MILP solvers. The effectiveness of the absorption model and the corresponding MILP-based MPC approach is illustrated through the case study based on two Beijing subway lines.