A remark on energy optimal strategies for a train movement

A remark on energy optimal strategies for a train movement

Článek recenzovaný mimo WoS a Scopus

This article introduces the notion of the critical time in the problem of the energy efficient train control and its calculation in some particular cases. We apply some results of non-linear parametric optimization to show that the number of optimal control levels depends on the relation between the given time of the journey and this critical time. Furthermore, we derive equations for the computation of the switching times. I emphasise exact forms of solutions with a minimal use of numerical mathematics. The results can be used to find the values of the switching times only by solving algebraic equations and to analyse the behaviour of the results with respect to given entry parameters of the problem.

This article introduces the notion of the critical time in the problem of the energy efficient train control and its calculation in some particular cases. We apply some results of non-linear parametric optimization to show that the number of optimal control levels depends on the relation between the given time of the journey and this critical time. Furthermore, we derive equations for the computation of the switching times. I emphasise exact forms of solutions with a minimal use of numerical mathematics. The results can be used to find the values of the switching times only by solving algebraic equations and to analyse the behaviour of the results with respect to given entry parameters of the problem.

critical time, optimal control, Pontryagin principle, switching time, nonlinear parametric optimization

critical time, optimal control, Pontryagin principle, switching time, nonlinear parametric optimization

POKORNÝ, P.

2010

05.08.2008

1446-8735

ANZIAM JOURNAL

50

E

Australské společenství

E1

E23

23