Reference
Y. Wang, B. De Schutter,
T. J. J.
van den Boom, and B. Ning, "Optimal trajectory planning for trains under fixed
and moving signaling systems using mixed integer linear programming,"
Control Engineering Practice, vol. 22, pp. 44-56, Jan. 2014.
Abstract
The optimal trajectory planning problem for multiple trains under fixed block
signaling systems and moving block signaling systems is considered. Two
approaches are proposed to solve this optimal control problem for multiple
trains: the greedy approach and the simultaneous approach. In each solution
approach, the trajectory planning problem is transformed into a mixed integer
linear programming (MILP) problem. In particular, the objective function
considered is the energy consumption of trains and the nonlinear train model is
approximated by a piece-wise affine model. The varying line resistance,
variable speed restrictions, and maximum traction force, etc. are also included
in the problem definition. In addition, the constraints caused by the leading
train in a fixed or moving block signaling system are first discretized and
then transformed into linear constraints using piecewise affine approximations
resulting in an MILP problem. Simulation results comparing the greedy MILP
approach with the simultaneous MILP approach show that the simultaneous MILP
approach yields a better control performance but requires a higher computation
time. Moreover, the performance of the proposed greedy and the proposed
simultaneous MILP approach is also compared with that of the greedy and the
simultaneous pseudospectral method, where the pseudospectral method is a
state-of-the-art method for solving optimal control problems. The results show
that the energy consumption and the end time violations of the greedy MILP
approach are slightly larger than those of the greedy pseudospectral method,
but the computation time is one to two orders of magnitude smaller. The same
trend holds for the simultaneous MILP approach and the simultaneous
pseudospectral method.
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BibTeX
@article{WanDeS:14-005,
author = {Wang, Yihui and De Schutter, Bart and van den Boom, Ton J. J. and
Ning, Bin},
title = {Optimal Trajectory Planning for Trains Under Fixed and Moving
Signaling Systems Using Mixed Integer Linear Programming},
journal = {Control Engineering Practice},
volume = {22},
pages = {44--56},
month = jan,
year = {2014}
}