An On-Line Optimal Controller for a Commuter Train

This paper proposes an on-board optimal controller that drives a train between two stations in an optimal time efficient, energy efficient, or mixed-objective manner, while adhering to a set of system-specific constraints. To this end, at each step along the track, the train control problem is formulated and solved as a constrained optimization problem over the remainder of the trip, while utilizing the latest train sensor data. The optimization problem is a convex second-order cone program. It incorporates knowledge of the track profile and relevant velocity and propulsion/braking constraints in the computation of the optimal propulsion/braking commands. It features an option to enforce a safety buffer between the train and another leading train on the track. The resulting convex optimization problem can be efficiently solved using a simple numerical solver, ensuring global optimality and robustness of the solution. Real-time performance and simulated closed-loop control results are presented, for a realistic vehicle and advanced trip model on desktop and embedded computer architectures.