考虑阻力约束的列车能量最优驾驶问题建模及分离迭代求解策略

Modeling for Train Energy Optimal Driving Problem with Resistance Constrains and Solving with Separation of Iteration Strategy

根据列车的动力学模型,牵引、制动特性,阻力,限速等条件,建立列车能量最优驾驶问题的数学模型。由于坡道阻力和运行阻力的引入,约束条件中的微分方程组(ODEs)增广成为复杂的微分代数方程组(DAEs),使得问题难以求解。首先在时间域内将状态变量和控制变量离散化,将问题转化为一般非线性规划问题;针对该非线性规划问题,提出一种分离迭代策略将其转化为一系列凸二次规划问题,最后采用原-对偶预测校正内点算法求解。算例结果表明,所提出的分离迭代策略在满足列车约束条件下可以实现能量消耗最小。

A mathematical model of train energy optimal driving problem was established according to the dynamics equations of train,traction,brake capability,resistance and speed limits.Due to the introduction of slope gradient resistance and running resistance,Ordinary Differential Equations(ODEs)in the constrains will be augmented into Differential-Algebraic Equations(DAEs),which results in more difficult solving of the problem.In order to solve this problem,the state and control variables were discretized in time domain,which transformed the original problem into a general nonlinear programming problem.To address the general nonlinear programming problem,a separation of iteration strategy was proposed to transform the problem into a series of convex quadratic programming problems.Finally,the convex quadratic programming problems were solved by applying primal-dual predictor-corrector interior-point algorithm.The numerical example results show that the proposed algorithm can obtain minimal energy consumption satisfying all the constrains.