Energy-Efficient Train Control Methods Based On Approximate Dynamic Programming In Urban Rail Transit

The rapid development of urban rail transit is accompanied by the increasingly serious energy consumption problem,and train’s traction energy consumption occupies a large proportion in the energy consumption of the whole system.By adjusting the control strategy in train operation,the traction energy consumption can be effectively reduced.Due to the control structure of the train operation system,this problem can be effectively solved by designing the optimal running curve and the optimal tracking controller aiming at reducing the traction energy consumption.This thesis first establishes the energy-efficient operation model in uraban rail transit and the maximum principle is used to analyze the theoretical properties of the optimal train control problem,related to five optimal controls and the switching rules of different modes.At the same time,the uniqueness problem of optimal trajectory without much exploration is studied considering speed limit and non-steep track.Several qualitative conclusions are given based on three typical cases.The conclusions can help get the uniquely optimal trajectory and the benefit is illustrated by simulation.The above theoretical results can be applied to the design of algorithms and the comparison of simulation in the later optimization algorithms.In order to solve the optimal train control problem,the previous energy-saving optimization model is modified,and the equivalence and necessity of the modification are theoretically explained.On top of that,the problem of solving the optimal switching position on the steep track is analyzed.The scenarios of steep uphill and steep downhill are studied and the dynamic programming algorithm is proposed.And the relationship is analyzed between the proposed algorithm and the local energy minimization principle.The simulation shows that the proposed algorithm can get the theoretically optimal solution.In general situations,based on approximate dynamic programming algorithm,a variety of function approximation methods are designed including the rollout algorithm,interpolation algorithm and neural network algorithm,and the corresponding updating methods of value function are given.The simulation results show that the interpolation algorithm can get the theoretically optimal solution in a relatively short time,and rollout algorithm achieves the least computation time with better performance compared with the basic strategy,and neural network algorithm takes the longest time.In order to solve the optimal tracking problem of the train,the tracking problem is first transformed into a regulation problem,and the performance index is designed considering the tracking error and energy consumption.The value iteration and policy iteration algorithms are put forward,as well as the corresponding solving processes and theoretical properties.In order to realize the above algorithms,the updating algorithms of control function are proposed based on gradient descent and contraction mapping,as well as the updating algorithms of value function based on least square method.And the above methods form four kinds of algorithms.Due to the saturation problem of control,a non-quadratic functional is introduced and the corresponding updating methods are built.Simulation results show that the proposed four algorithms can achieve the same optimal solution,and the performance index is significantly better than that of initial PID controller and the controller designed by feedback linearization,especially in the case where the approximate dynamic programming controllers achieve lower energy consumption and tracking error in tracking the speed curve.And the proposed non-quadratic functional method can effectively solve the saturation problem of control.