Speed profile optimization of an electrified train in Cat Linh-Ha Dong metro line based on pontryagin's maximum principle

An urban railway is a complex technical system that consumes large amounts of energy, but this means of transportation still has been obtained more and more popularity in densely populated cities because of its features of high-capacity transportation capability, high speed, security, punctuality, lower emission, reduction of traffic congestion. The improved energy consumption and environment are two of the main objectives for future transportation. Electrified trains can meet these objectives by the recuperation and reuse of regenerative braking energy and by the energy - efficient operation. Two methods are to enhance energy efficiency: one is to improve technology (e.g., using energy storage system, reversible or active substations to recuperate regenerative braking energy, replacing traction electric motors  by energy-efficient traction system as permanent magnet electrical motors; train's mass reduction by lightweight material mass...); the other is to improve operational procedures (e.g. energy efficient driving including: eco-driving; speed profile optimization; Driving Advice System (DAS); Automatic Train Operation (ATO); traffic management optimization...). Among a lot of above solutions for saving energy, which one is suitable for current conditions of metro lines in Vietnam. The paper proposes the optimization method based on Pontryagin's Maximum Principle (PMP) to find the optimal speed profile for electrified train of Cat Linh-Ha Dong metro line, Vietnam in an effort to minimize the train operation energy consumption.