Optimization for train speed trajectory based on Pontryagin's Maximum Principle

Bao, Kai; Lu, Shaofeng; Xue, Fei; Tan, Zhaoxiang

doi:10.1109/itsc.2017.8317820

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…In our proposed numerical algorithms, we are to apply linear iteration using the corresponding co-state equations in each case and use a simple intuitive search method to search for the initial and final co-state variable values, or the initial and final distances. The linear iteration is based on a sufficiently small distance step ∆d ( [52]).…”

Section: Case V θ Dθ Dxmentioning

confidence: 99%

“…Equation 51ensures the maximum kinetic energy reduction is no more than the one caused by the maximum braking effort. Equation (52) guarantees that the maximum kinetic energy increase is no more than the one caused by the maximum tractive effort. In such a way, the first two equations ensure the maximum tractive/braking efforts are not exceeded.…”

Section: Speed Distancementioning

confidence: 99%

“…N are the determining variables and the objective function is to minimize the total net energy consumption from the electrical motor as defined in Equation (33). We consider that no mechanical braking effort to enable a comparison with the method based on the PMP but other means of braking can be incorporated in the model by updating the constraints during braking in Equations (52) and Equation (54) using the maximum braking rate ( [6,46]).…”

Section: Speed Distancementioning

confidence: 99%

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Adaptive Partial Train Speed Trajectory Optimization

Tan

Bao

et al. 2018

Energies

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Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.

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Section: Case V θ Dθ Dxmentioning

confidence: 99%

Section: Speed Distancementioning

confidence: 99%

Section: Speed Distancementioning

confidence: 99%

See 1 more Smart Citation

Adaptive Partial Train Speed Trajectory Optimization

Tan

Bao

et al. 2018

Energies

Self Cite

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“…Pontryagin's maximum principle (PMP) was used to solve the problem of optimal train speed profile planning for different driving conditions in Refs. [9,10]. A real-time strategy for speed planning based on PMP and Lagrange multiplier technique was proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Energy-Saving and Punctuality Combined Velocity Planning for the Autonomous-Rail Rapid Tram with Enhanced Pseudospectral Method

Wang

Han

Yan

et al. 2023

Chin. J. Mech. Eng.

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Autonomous-rail rapid transit (ART) is a new medium-capacity rapid transportation system with punctuality, comfort and convenience, but low-cost construction. Combined velocity planning is a critical approach to meet the requirements of energy-saving and punctuality. An ART velocity pre-planning and re-planning strategy based on the combination of punctuality dynamic programming (PDP) and pseudospectral (PS) method is proposed in this paper. Firstly, the longitudinal dynamics model of ART is established by a multi-particle model. Secondly, the PDP algorithm with global optimal characteristics is adopted as the pre-planning strategy. A model for determining the number of collocation points of the real-time PS method is proposed to improve the energy-saving effect while ensuring computation efficiency. Then the enhanced PS method is utilized to design the velocity re-planning strategy. Finally, simulations are conducted in the typical scenario with sloping roads, traffic lights, and intrusion of the pedestrian. The simulation results indicate that the ART with the proposed velocity trajectory optimization strategy can meet the punctuality requirement, and obtain better economy efficiency compared with the punctuality green light optimal speed advisory (PGLOSA).

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“…The minimization of consumed traction energy based on PMP offers [9]. For a simplified train model, which has no speed limit, gradient, and regenerative braking, five subsequent control modes are supposed: maximum traction, partial traction, coasting, partial braking, and maximum braking.…”

Section: Introductionmentioning

confidence: 99%

Exploitation of Energy Optimal and Near-Optimal Control for Traction Drives with AC Motors

et al. 2022

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The main contribution of this paper is the verification of a new train control system applied to the drive with a.c. motors that is energy near optimal with respect to electrical and mechanical energy minimization. All simulations are related to the one traction motor yielding its best exploitation. Load torque treated as a state variable consists of constant, linear, and quadratic components as a function of rotor speed. The required performance of the energy-saving control is rendered straightforward using precomputed energy optimal state variables or a prediction of losses for a symmetrical trapezoidal speed profile as the second alternative. An energy-saving reference position generator provides the state variables, which are faithfully followed by a feedback control based on field orientation, which is completed with a matched zero dynamic lag pre-compensator yielding prescribed closed-loop dynamics. Simulation results mutually compared confirm the capability of an overall drive control system to follow generated state variables for two different service conditions and the possibility of energy savings.

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Optimization for train speed trajectory based on Pontryagin's Maximum Principle

Cited by 6 publications

References 7 publications

Adaptive Partial Train Speed Trajectory Optimization

Adaptive Partial Train Speed Trajectory Optimization

Energy-Saving and Punctuality Combined Velocity Planning for the Autonomous-Rail Rapid Tram with Enhanced Pseudospectral Method

Exploitation of Energy Optimal and Near-Optimal Control for Traction Drives with AC Motors

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