Cooperative train control during the power supply shortage in metro system: A multi-agent reinforcement learning approach

In metro system, the fault of traction power supply system may cause the power supply shortage around the failure substation. In this case, the dispatching measure should be immediately taken to reduce the impacts of disruption on the train operation. To deal with this real-time traffic management problem, a cooperative control approach is proposed in this paper. In this approach, the time to apply tractive force and the level of force are simultaneously adjusted for all the operated trains, to maximize the maintained line capacity when considering the power supply capacity. Compared with the existing train timetable rescheduling approach, cooperative control is more flexible to get a better train regulation solution. To solve the challenges for developing the cooperative control model (i.e., undetermined number and dynamically changing of controlled objects), an imaginary section method is newly developed to transform the original problem into an equivalent cooperative control problem with fixed controlled objects. Then, the mathematical models for the transformed problem are constructed by using the space-time-speed network methodology. According to the formulated model, a Decentralized-Markov Decision Process (Dec-MDP) framework is designed as the basis of the applied algorithm. Next, a Collaboration Mechanism Based-Independent Deep Q-Network (CMB-IDQN) algorithm is proposed to solve the cooperative control problem. Compared with classical IDQN algorithm, a credit assignment method based on the collaboration mechanism among trains is novelly considered in the designed multi-agent reinforcement learning algorithm. Finally, the effectiveness of the proposed cooperative control approach is verified by two case studies. When solving the cooperative control problem, the performance by using CMB-IDQN algorithm can be increased by up to 13.0% and 16.8% compared with other two classical reinforcement learning algorithms (i.e., DQN and IDQN), respectively. Compared with two train timetable rescheduling measures during the power supply shortage, the cooperative control approach can improve the solution quality by more than 180.4% and 17.4%, respectively.