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Adaptive Numerical Approach for Optimal Control of a Single Train

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Abstract

This paper considers the optimal control problem of a single train, which is formulated as an optimal control problem of nonlinear systems with switching controller. The switching sequence and the switching time are decision variables to be chosen optimally. Generally speaking, it is very difficult to solve this problem analytically due to its nonlinear nature, the complexity of the controller, and the existence of system state and control input constraints. To obtain the numerical solution, by introducing binary functions for every value of the control input, relaxing the binary functions, and imposing a penalty function on the relaxation, the problem is transformed into a parameter optimization problem, which can be efficiently solved by using any gradient-based numerical approach. Then, the authors propose an adaptive numerical approach to solve this problem. Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem. Finally, an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches.

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Xiang Wu

  2. School of Electrical Engineering, Southeast University, Nanjing, 210096, China

    Xiang Wu & Ming Cheng

  3. School of Automation, Southeast University, Nanjing, 210096, China

    Kanjian Zhang

  4. Key Laboratory of Measurement and Control of CSE, Ministry of Education, Southeast University, Nanjing, 210096, China

    Kanjian Zhang

Authors
  1. Xiang Wu
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  2. Kanjian Zhang
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  3. Ming Cheng
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Corresponding author

Correspondence to Xiang Wu.

Additional information

This work was supported by the Chinese National Natural Science Foundation under Grant Nos. 61563011, 61473158, 61703012, and 61374006, and the Ph.D Research Fund of Guizhou Normal University under Grant No. 11904–0514170.

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Wu, X., Zhang, K. & Cheng, M. Adaptive Numerical Approach for Optimal Control of a Single Train. J Syst Sci Complex 32, 1053–1071 (2019). https://doi.org/10.1007/s11424-018-7277-7

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  • DOI: https://doi.org/10.1007/s11424-018-7277-7

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