Pseudospectral optimal train control

In the last decade, pseudospectral methods have become popular for solving optimal control problems. Pseudospectral do not need prior knowledge about structure and are thus very flexible problems with complex path constraints, which common in train control, or trajectory optimization. Practical nonsmooth discontinuities dynamic equations constraints corresponding to gradients speed limits varying along track. Moreover, typically include singular solutions a vanishing Hessian of associated Hamiltonian. These characteristics make these hard solve also lead convergence issues methods. We propose computational framework that connects Pontryagin’s Maximum Principle allowing computations, verification validation numerical approximations, improvements continuous solution accuracy. apply two basic control: minimum-time energy-efficient consider cases short-distance regional trains long-distance intercity various scenarios including gradients, limits, scheduled running time supplements. The confirms flexibility method regards state, mixed algebraic inequality is able identify conditions inconsistencies between necessary optimality approximations states, costates, controls. A new approach proposed correct discrete by incorporating implicit from conditions. particular, issue oscillations driving as computed has been solved.