S. Li, B. De Schutter, L. Yang, and Z. Gao, "Robust model predictive control for train regulation in underground railway transportation," IEEE Transactions on Control Systems Technology, vol. 24, no. 3, pp. 1075-1083, May 2016.
This paper investigates the robust model predictive control for train regulation in underground railway transportation. By considering the uncertain passenger arrival flow, a constrained state-space model for the train traffic of a metro loop line is developed. The goal of the paper is to design a state-feedback control law at each decision step to optimize a metro system cost function subject to safety constraints on the control input. Based on Lyapunov function theory, the problem of optimizing an upper bound on the system cost function subject to input constraints is reduced to a convex optimization problem involving linear matrix inequalities (LMIs). Moreover, for the inevitable disturbances leading to the delays, the robust model predictive control strategy of train regulation is designed for a metro loop line such that it ensures the minimization of an upper bound on metro system cost function, and meanwhile guarantees a disturbance attenuation level with respect to the disturbances. Numerical examples are given to illustrate the effectiveness of the proposed methods.