Optimal switched control design for automatic train regulation of metro lines with time-varying passengers arrival flow

This paper investigates the optimal switched control design problem for automatic train regulation of metro lines with time-varying passengers arrival flow. The variation of passenger arrival flow is described by an uncertain switched linear function. A new train traffic model of the metro-line operation is proposed based on an uncertain switched hybrid system. According to the stability analysis method of the switched system, a sufficient condition for the existence of state-feedback control as automatic train regulation strategy is given in terms of matrix inequalities, which ensures the stability of metro line system under a disturbance or a disruption. Moreover, a nonlinear optimal control problem is formulated to determine the optimal switched control design as automatic train regulation to minimize the train delays and control cost. The formulated nonlinear optimal control problem is converted into a convex optimization problem involving linear matrix inequalities, which can be solved in polynomial time and has low computation burden. Numerical examples are given to illustrate the effectiveness of the proposed methods.