The key principles of optimal train control—Part 1: Formulation of the model, strategies of optimal type, evolutionary lines, location of optimal switching points

Albrecht, Amie; Howlett, Phil; Pudney, Peter; Vu, Xuan; Zhou, Peng

doi:10.1016/j.trb.2015.07.023

Cited by 241 publications

(142 citation statements)

References 18 publications

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“…The stochastic perturbations are added in the system dynamics (6). The maximum amplitude of the perturbation is assumed to be 1.…”

Section: Stochastic Perturbationsmentioning

confidence: 99%

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Optimal Operation of High-Speed Trains Using Hybrid Model Predictive Control

Yang

Liu

et al. 2018

Journal of Advanced Transportation

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The high-speed train operation process is highly nonlinear and has multiple constraints and objectives, which lead to a requirement for the automatic train operation (ATO) system. In this paper, a hybrid model predictive control (MPC) framework is proposed for the controller design of the ATO system. Firstly, a piecewise linear system with state and input constraints is constructed through piecewise linearization of the high-speed train's nonlinear dynamics. Secondly, the piecewise linear system is transformed into a mixed logical dynamical (MLD) system by introducing the auxiliary binary variables. For the transformed MLD system, a hybrid MPC controller is designed to realize the precise control under hard constraints. To reduce the online computation complexity, the explicit control law is computed offline by employing the mixed-integer linear programming (MILP) technique. Simulation results validate the effectiveness of the proposed method.

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“…The stochastic perturbations are added in the system dynamics (6). The maximum amplitude of the perturbation is assumed to be 1.…”

Section: Stochastic Perturbationsmentioning

confidence: 99%

“…Currently, the researches of automatic train control are mainly based on single-point model and multipoint model [6]. For single-point model, the whole high-speed train is simplified as a single rigid mass point, which ignores the coupling characteristics among the vehicles and the allocation of the distributed traction/brake force.…”

Section: Introductionmentioning

confidence: 99%

Optimal Operation of High-Speed Trains Using Hybrid Model Predictive Control

Yang

Liu

et al. 2018

Journal of Advanced Transportation

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“…The expected speedholding operation is not perfectly realized; instead, it is approximated by a mixture of coast-power pairs and speedholding. It might be because that the speedholding corresponds to the singular arc of the train control problem given in Section 2 (Albrecht et al, 2015b;Howlett, 2000;Khmelnitsky, 2000;Liu and Golovitcher, 2003), and it has been known that the singular arc may not be perfectly estimated by the so-called direct method including RPM for solving the optimal control problems (Betts, 2010;Garg, 2011;Patterson and Rao, 2014;Rao et al, 2010). To obtain a high-accuracy speedholding operation by RPM, one may explicitly provide the singular arc conditions as path constraints (Betts, 2010;Patterson and Rao, 2014) in the original optimal control formulation.…”

Section: Case Studiesmentioning

confidence: 99%

“…To obtain a high-accuracy speedholding operation by RPM, one may explicitly provide the singular arc conditions as path constraints (Betts, 2010;Patterson and Rao, 2014) in the original optimal control formulation. Regarding this, Howlett et al (2009) and Albrecht et al (2015bAlbrecht et al ( , 2015c have proposed explicit numerical methods that can be used to find the initial and final points of a singular speedholding phase; however, it requires and is worth further investigation in the future whether their method can be combined with RPM and help identify the speedholding phases under the complex settings in this paper with multiple trains and/or multiple nodes.…”

Section: Case Studiesmentioning

confidence: 99%

“…However, this framework can face challenges in a complex and busy railway network. As it was argued by Albrecht et al (2015b), "… the most pressing research challenges for the future in this area are to develop optimal control policies for trains travelling in the same direction on the same line in such a way that safe separation is maintained between trains. On busy rail networks, solution of the train separation problem relates to and depends on integrated scheduling and control policies to ensure that train movements are both energy-efficient and effectively coordinated.…”

Section: Introductionmentioning

confidence: 99%

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A multiphase optimal control method for multi-train control and scheduling on railway lines

Liu

2016

Transportation Research Part B: Methodological

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We consider a combined train control and scheduling problem involving multiple trains in a railway line with a predetermined departure/arrival sequence of the trains at stations and meeting points along the line. The problem is formulated as a multiphase optimal control problem while incorporating complex train running conditions (including undulating track, variable speed restrictions, running resistances, speed-dependent maximum tractive/braking forces) and practical train operation constraints on departure/arrival/running/dwell times.Two case studies are conducted. The first case illustrates the control and scheduling problem of two trains in a small artificial network with three nodes, where one train follows and overtakes the other. The second case optimizes the control and timetable of a single train in a subway line. The case studies demonstrate that the proposed framework can provide an effective approach in solving the combined train scheduling and control problem for reducing energy consumption in railway operations.

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Research on multi‐train energy saving optimization based on cooperative multi‐objective particle swarm optimization algorithm

et al. 2020

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Summary An energy saving optimization method of multi‐train collaboration is studied. According to the different scenarios of two and three trains, the corresponding overlapping time calculation model was established respectively. Minimizing the total energy consumption, a multi‐train collaborative energy consumption optimization model is established. The cooperative multi‐objective PSO algorithm was used to solve the model from the aspects of optimizing stop time and departure interval as well as the train speed curve. Finally, the energy optimization of the whole line of multi‐train during the morning rush hour were carried out by the actual data of Guangzhou metro line 7. The results show that the optimization model can greatly improve the utilization efficiency of regenerative energy and save energy consumption of the whole line by 11.74%.

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The key principles of optimal train control—Part 1: Formulation of the model, strategies of optimal type, evolutionary lines, location of optimal switching points

Cited by 241 publications

References 18 publications

Optimal Operation of High-Speed Trains Using Hybrid Model Predictive Control

Optimal Operation of High-Speed Trains Using Hybrid Model Predictive Control

A multiphase optimal control method for multi-train control and scheduling on railway lines

Research on multi‐train energy saving optimization based on cooperative multi‐objective particle swarm optimization algorithm

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