Distributed optimal control for multiple high-speed train movement: An alternating direction method of multipliers

Abstract

This study systematically investigates the distributed optimal control of multiple high-speed train movement to overcome communication constraints and realize efficient speed control. A dynamic multiple train movement model is constructed to capture the dynamic evolution of trains in real-world operations. With the coupling constraints for the safe distance headway among neighboring trains, an optimal control problem is formulated to improve speed and distance tracking accuracy for each train and reduce energy consumption. Based on the dual decomposition technique, each train is regarded as a subsystem equipped with a local controller while a centralized entity manages the subsystem via the prices associated with the coupling constraints. Within the framework of an alternating direction method of multipliers and a model predictive control method, a novel distributed optimal control algorithm based on a distributed message passing mechanism is designed. The algorithm divides the original complex optimal control problem into many smaller optimal control problems that can be computed in parallel and satisfies the real-time control requirement. Numerical examples are provided to illustrate the effectiveness of the proposed train control model and methods.