Optimal control of a subway train with regard to the criteria of minimum energy consumption

Баранов, Л. А.; Meleshin, I. S.; Chin, Lee M.

doi:10.3103/s1068371211080049

Cited by 21 publications

(9 citation statements)

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“…There are several widely cited papers which propose analytic solutions to the classic single train control problem in which one wishes to find a strategy that minimizes tractive energy consumption but allows the train to complete the journey within a maximum allowed journey time but with no intermediate time constraints. The standard references to this work when continuous control is allowed are the papers by Albrecht et al [1,4,5], Baranov et al [14], Howlett [33,39], Howlett et al [41], Khmelnitsky [47] and Liu and Golovitcher [54]. Other significant studies in the Russian literature [12,13,[25][26][27][28]45] and some early works [44,48,57,62] may be difficult to obtain and the relevant results can usually be extracted from more recent papers.…”

Section: Previous Workmentioning

confidence: 99%

Optimal Driving Strategies for Two Successive Trains on Level Track With Safe Separation

Albrecht

Howlett

Pudney

2022

IEEE Trans. Intell. Transport. Syst.

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We investigate analytic solutions to the problem of finding driving strategies which minimize total tractive energy consumption subject to constraints that ensure safe separation for a fleet of trains travelling on the same track in the same direction and minimize line occupancy time span for the fleet. It is known that a fleet of trains can be safely separated if intermediate signal times are prescribed by inequality constraints for each train at each signal location. The optimal driving strategy for each train is then uniquely defined by an optimal driving speed on each actively timed segment. The problem of finding optimal intermediate times has been solved for a fleet of two trains but for more than two trains the problem rapidly becomes intractable as the number of trains and signals increases. The main difficulty is in distinguishing between active and inactive constraints. This is exacerbated by the fact that an inactive constraint with one set of prescribed times may become active if the set of prescribed times changes. The curse of dimensionality means it is not feasible to check every different combination of designated active and inactive constraints and to optimize the corresponding prescribed times. Nevertheless we can formulate a substantial optimization problem with intermediate signal times prescribed by active equality constraints for all trains in the fleet. We find necessary and sufficient conditions on the optimal times and demonstrate viable solution algorithms to find the associated optimal speed profiles for each train. Compared to the schedule required for safe separation when each train uses the classic single-train optimal strategy our method provides a substantial reduction in the line occupancy time span with only a minimal increase in journey costs.

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Section: Previous Workmentioning

confidence: 99%

Optimal Driving Strategies for Two Successive Trains on Level Track With Safe Separation

Albrecht

Howlett

Pudney

2022

IEEE Trans. Intell. Transport. Syst.

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“…We will not attempt a comprehensive review of the wellestablished and clearly defined theoretical work on optimal control of a single train. For details of the underlying theory we refer readers to the frequently cited papers on discrete control [15,26,29,31,33] and the key references on continuous control [1,2,5,6,11,27,28,34,37,41,48]. The early papers on continuous control [9,25,35,38,44,46] contain some important insights but are not directly related to this paper.…”

Section: Previous Workmentioning

confidence: 99%

The Two-Train Separation Problem on Level Track With Discrete Control

Howlett¹

2018

ANZIAM J.

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When two trains travel along the same track in the same direction, it is a common safety requirement that the trains must be separated by at least two signals. This means that there will always be at least one clear section of track between the two trains. If the safe-separation condition is violated, then the driver of the following train must adopt a revised strategy that will enable the train to stop at the next signal if necessary. One simple way to ensure safe separation is to define a prescribed set of latest allowed section exit times for the leading train and a corresponding prescribed set of earliest allowed section entry times for the following train. We will find strategies that minimize the total tractive energy required for both trains to complete their respective journeys within the overall allowed journey times and subject to the additional prescribed section clearance times. We assume that the drivers use a discrete control mechanism and show that the optimal driving strategy for each train is defined by a sequence of approximate speedholding phases at a uniquely defined optimal driving speed on each section and that the sequence of optimal driving speeds is a decreasing sequence for the leading train and an increasing sequence for the following train. We illustrate our results by finding optimal strategies and associated speed profiles for both trains in some elementary but realistic examples.

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“…A remarkable result from their model was that no maximum acceleration or maximum braking is applied at high speeds due to the nonlinear power losses. Baranov et al (2011) considered the EETC problem with both mechanical and regenerative braking with distance as independent variable. Denote by u f , u b and u r the mass-specific force due to traction, braking and regenerative braking, respectively.…”

Section: Exact Methods With Regenerative Brakingmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

333

149

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The energy consumption of trains is highly efficient due to the low friction between steel wheels and rails, although the efficiency is also influenced largely by the driving strategy applied and the scheduled running times in the timetable. Optimal energy-efficient driving strategies can reduce operating costs significantly and contribute to a further increase of the sustainability of railway transportation. The railway sector hence shows an increasing interest in efficient algorithms for energy-efficient train control, which could be used in real-time Driver Advisory Systems (DAS) or Automatic Train Operation (ATO) systems. This paper gives an extensive literature review on energy-efficient train control (EETC) and the related topic of energy-efficient train timetabling (EETT), from the first simple models from the 1960s of a train running on a level track to the advanced models and algorithms of the last decade dealing with varying gradients and speed limits, and including regenerative braking. Pontryagin's Maximum Principle (PMP) has been applied intensively to derive optimal driving regimes that make up the optimal energy-efficient driving strategy of a train under different conditions. Still, the optimal sequence and switching points of the optimal driving regimes are not trivial in general, which led to a wide range of optimization models and algorithms to compute the optimal train trajectories and more recently to use them to optimize timetables with a trade-off between energy efficiency and travel times.

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Optimal control of a subway train with regard to the criteria of minimum energy consumption

Cited by 21 publications

References 0 publications

Optimal Driving Strategies for Two Successive Trains on Level Track With Safe Separation

Optimal Driving Strategies for Two Successive Trains on Level Track With Safe Separation

The Two-Train Separation Problem on Level Track With Discrete Control

Review of energy-efficient train control and timetabling

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