Optimal trajectory planning for a single train

Abstract

In this chapter, the optimal trajectory planning problem for the operation of a single train under various constraints and with a fixed arrival time is considered. The objective function corresponds to a trade-off between the energy consumption and the riding comfort. Two approaches are proposed to solve this optimal control problem, viz. a pseudospectral method and a mixed integer linear programming (MILP) approach. 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. For the MILP approach, the optimal trajectory planning problem is reformulated as an MILP problem by approximating the nonlinear terms by piecewise affine functions. The performance of these two approaches is compared through a case study. The work discussed in this chapter is based on Wang et al. (Proceedings of the 14th international IEEE conference on intelligent transportation systems (ITSC 2011). Washington DC, USA, pp 1598-1604, 2011) [1]; Wang et al. (Transp Res Part C 29: 97-114, 2013) [2]; Wang et al. (Proceedings of the 13th IFAC symposium on control in transportation systems (CTS’2012). Sofia, Bulgaria, pp 158-163, 2012) [3].