Optimal Guaranteed Cost Cruise Control for High-Speed Train Movement

In this paper, the optimal guaranteed cost cruise control for high-speed train movement with uncertain parameters and control constraints is investigated. Sufficient condition for the existence of guaranteed cost cruise control law is given in terms of linear matrix inequalities, under which each car of the high-speed train tracks the desired speed, the relative spring displacement is stable at the equilibrium state, and meanwhile an upper bound of the train performance is guaranteed. Moreover, a convex optimization problem is formulated to determine the optimal guaranteed cost control law that minimizes an upper bound on the train performance (energy consumption and tracking error). Numerical examples are given to illustrate the effectiveness of the proposed methods.