Pseudospectral Real-Time Optimal Energy Control with Safety Constraints for Heavy-Haul Trains

Heavy-haul trains must be energy-efficient and safe during their operations. Owing to the multidimensional high-order nonlinear characteristic of heavy-haul trains, which include numerous cars, this paper proposes a uniform pseudospectral real-time closed-loop optimal control framework to minimize the energy consumption with control inputs and state constraints based on the Radau Pseudospectral Method (RPM). In the framework, in order to ensure safe running of the heavy-haul train, the desired in-train force and speed limit requirements are formulated as constraints of optimal control. Simultaneously, a constrained closed-loop optimal control is constructed by using the receding horizon control principle and pseudospectral observer, in which RPM is leveraged to obtain real-time optimal solutions. The effectiveness of the proposed approach is verified from simulation results.