Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming

Oleg Valinsky; Andrey Evstaf&#039;ev; Anton Sychugov; Evgeniy Suhanov

doi:10.20295/2223-9987-2026-2-7-21

UDC

629.4.053

CONSTRUCTION OF AN OPTIMAL MOTION MODEL FOR A HIGH-SPEED ELECTRIC TRAIN BASED ON PRECOMPUTED TRANSITIONS AND DYNAMIC PROGRAMMING Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming

АА Аа

Published in Bulletin of scientific research results · Pages 7–21 · Rubric: PROBLEMATIC OF TRANSPORT SYSTEM

DOI: https://doi.org/10.20295/2223-9987-2026-2-7-21

Received: 10.04.2026 Accepted: 06.05.2026 Published: 29.06.2026

Authors

Oleg Valinsky

Andrey Evstaf'ev

Anton Sychugov

Evgeniy Suhanov

Oleg Valinsky

Academic degree: candidate of technical sciences

Science rang: professor

Emperor Alexander I St. Petersburg State Transport University Rector · Russian Federation · Saint-Petersburg

Andrey Evstaf'ev

Academic degree: doctor of technical sciences

Science rang: professor

Emperor Alexander I St. Petersburg State Transport University Head of the Department · Department of Electric Traction · Russian Federation

Anton Sychugov

Academic degree: candidate of technical sciences

Emperor Alexander I St. Petersburg State Transport University Associate Professor · Russian Federation · Saint-Petersburg

Evgeniy Suhanov

Emperor Alexander I St. Petersburg State Transport University Postgraduate Student · Russian Federation · St. Petersburg

ABSTRACT

Objective: to construct an optimal motion model for a high-speed electric train along a given line section, ensuring coordinated compliance with the timetable, speed limits and stopping conditions on the basis of a developed automatic train operation model, precomputed motion transition characteristics and a recursive dynamic programming procedure. Methods: the study employs a developed automatic train operation model of a high-speed electric train, a segment-based representation of the line section, precomputation of motion transition characteristics and the dynamic programming method. The proposed approach makes it possible to separate the stage of preliminary formation of motion transition characteristics from the stage of optimization-based decision making. For each track segment and each admissible set of input states, the passage results are determined in advance in the form of running time and exit speed, after which stepby- step selection of speed-control restrictions is performed using the Bellman recursive relation. Results: an algorithm for constructing an optimal motion model of a high-speed electric train has been developed, it ensures coordinated timetable compliance while preserving the operational automatic train operation model as the computational basis. It is shown that the use of precomputed transitions makes it possible to connect a complex longitudinal motion model with an optimization-based decision-making procedure and to obtain a computational model suitable for further application within automatic train operation algorithms. Simulation results are presented that confirm a small discrepancy between the solution obtained by the dynamic programming method and direct motion simulation performed on the automatic train operation model. Practical importance: the proposed approach can be used in the development of automatic train operation algorithms for high-speed electric trains aimed at timetable compliance, improving motion control stability, and forming a substantiated train motion model for a given line section.

KEYWORDS

high-speed electric train, traffic schedule, automatic train control system, dynamic programming, Bellman relation, speed limit, motion optimization

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GOST

Valinsky O. S., Evstaf'ev A. M., Sychugov A. N., Suhanov E. V. Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming // Bulletin of scientific research results. 2026. no. 2. pp. 7-21. DOI: https://doi.org/10.20295/2223-9987-2026-2-7-21. (Date of access 08.09.2026).

MLA

Oleg Valinsky, Evstaf'ev A. M., Sychugov A. N., Suhanov E. V.. "Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming." Bulletin of scientific research results 2026.2 (2026): 7-21. DOI: https://doi.org/10.20295/2223-9987-2026-2-7-21.

APA

Valinsky O. S., Evstaf'ev A. M., Sychugov A. N., Suhanov E. V. (2026). Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming. Bulletin of scientific research results, 2026(2), 7-21. https://doi.org/10.20295/2223-9987-2026-2-7-21

Chicago

Oleg Valinsky, Evstaf'ev A. M., Sychugov A. N., Suhanov E. V.. "Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming." Bulletin of scientific research results 2026, no. 2 (2026): 7-21. https://doi.org/10.20295/2223-9987-2026-2-7-21.

WIKI

{{cite journal | author = Valinsky O. S., Evstaf'ev A. M., Sychugov A. N., Suhanov E. V. | title = Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming | journal = Bulletin of scientific research results | year = 2026 | volume = 2026 | issue = 2 | pages = 7-21 | doi = 10.20295/2223-9987-2026-2-7-21 }}

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CONSTRUCTION OF AN OPTIMAL MOTION MODEL FOR A HIGH-SPEED ELECTRIC TRAIN BASED ON PRECOMPUTED TRANSITIONS AND DYNAMIC PROGRAMMING Construction of an Optimal Motion Model for a High-Speed Electric Train Based on Precomputed Transitions and Dynamic Programming

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