Cooperative Control of Maglev Levitation System via Hamiton-Jacobian-Bellman Multi-Agent Deep Reinforcement Learning

Qi Zhu, Su Mei Wang, Yi Qing Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review


The magnetic levitation control system is a key component of a maglev train, ensuring that the airgap between the train and its guideway is stable. Currently, the levitation controller is designed based on a single-point model in which the coupling effect between two levitation units at one side of the bogie in the maglev train is ignored. However, it is found that the coupling effect can cause unstable levitation problems during long-term operations. Hence, to solve the coupling problem of the two levitation units, a cooperative levitation controller based on the Hamiton-Jacobian-Bellman incorporated multi-agent reinforcement learning (HJB–MADRL) is proposed. The MADRL is adopted for the two-point levitation control considering the coupling effect between the two levitation units. To improve the training of the value network in the MADRL, the HJB function is used in control theory to evaluate the optimality of the value function. The proposed algorithm shows an improved performance compared to the original MADRL algorithm. The effectiveness of the proposed cooperative controller using the proposed algorithm is verified by comparing with a conventional proportional-integral-derivatve (PID) controller and a model-guided controller. The robustness of the HJB–MADRL controller is examined in the presence of pitch motion, change in train load, disturbance force, and track irregularity.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalIEEE Transactions on Vehicular Technology
Publication statusAccepted/In press - 2024


  • Control systems
  • Cooperative control Hamiton-Jacobian-Bellman function
  • Couplings
  • Levitation
  • Maglev levitation system
  • Magnetic levitation vehicles
  • Mathematical models
  • MIMO communication
  • multi-agent reinforcement learning
  • Training

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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