Reference
Y. Wang, B. De Schutter,
T. J. J.
van den Boom, and B. Ning, "Optimal trajectory planning for trains - A
pseudospectral method and a mixed integer linear programming approach,"
Transportation Research Part C, vol. 29, pp. 97-114, Apr.
2013.
Abstract
The optimal trajectory planning problem for train operations under constraints
and fixed arrival time is considered. The varying line resistance, variable
speed restrictions, and varying maximum traction force are included in the
problem definition. The objective function is a trade-off between the energy
consumption and the riding comfort. Two approaches are proposed to solve this
optimal control problem. First, we propose to use the pseudospectral method, a
state-of-the-art method for optimal control problems, which has not used for
train optimal control before. In the pseudospectral method, the optimal
trajectory planning problem is recast into a multiple-phase optimal control
problem, which is then transformed into a nonlinear programming problem.
However, the calculation time for the pseudospectral method is too long for the
real-time application in an automatic train operation system. To shorten the
computation time, the optimal trajectory planning problem is reformulated as a
mixed-integer linear programming (MILP) problem by approximating the nonlinear
terms in the problem by piecewise affine functions. The MILP problem can be
solved efficiently by existing solvers that guarantee to return the global
optimum for the proposed MILP problem. Simulation results comparing the
pseudospectral method, the new MILP approach, and a discrete dynamic
programming approach show that the pseudospectral method has the best control
performance, but that if the required computation time is also take into
consideration, the MILP approach yields the best overall performance. More
specifically, for the given case study the control performance of the
pseudospectral approach is about 10% better than that of the MILP approach, and
the computation time of the MILP approach is two to three orders of magnitude
smaller than that of the pseudospectral method and the discrete dynamic
programming approach.
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BibTeX
@article{WanDeS:13-004,
author = {Wang, Yihui and De Schutter, Bart and van den Boom, Ton J. J. and
Ning, Bin},
title = {Optimal Trajectory Planning for Trains -- {A} Pseudospectral
Method and a Mixed Integer Linear Programming Approach},
journal = {Transportation Research Part C},
volume = {29},
pages = {97--114},
month = apr,
year = {2013}
}