Joint optimal train regulation and passenger flow control strategy for high-frequency metro lines

To improve the headway regularity and commercial speed of high-frequency metro lines with overloaded passenger flow, this paper systematically investigates a joint optimal dynamic train regulation and passenger flow control design for metro lines. A coupled state-space model for the evolution of the departure time and the passenger load of each train at each station is explicitly developed. The dwell time of the train is affected by the number of entering and exiting passengers. Combining dynamic train regulation and passenger flow control, a dynamic optimisation problem that minimises the timetable and the headway deviations for metro lines is developed. By applying a model predictive control (MPC) method, we formulate the problem of finding the optimal joint train regulation and passenger flow control strategy as the problem of solving a set of quadratic programming (QP) problems, under which an optimal control law can be numerically calculated efficiently using a quadratic programming algorithm. Moreover, based on the Lyapunov stability theory, the stability (convergence) of the metro line system under the proposed optimal control algorithm is verified. Numerical examples are given to illustrate the effectiveness of the proposed method