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<p>In this article, a robust model predictive control (MPC) approach based on reinforcement learning (RL) techniques and adaptive critic designs is established to address zero-sum game problems of complex systems with disturbances. During the real-time interaction between the environment and the agent, a formidable challenge is posed for maintaining the stable operation of systems due to the disturbances caused by the environment, which is regarded as a two-player zero-sum game problem of nonlinear MPC (NMPC) in this article. According to the intelligent critic mechanism, the RL-based robust NMPC (RL-rNMPC) framework is first constructed to resolve the Nash equilibrium strategies. It is worth mentioning that the relaxed iteration scheme is introduced to expedite the iteration process within each prediction horizon. Meanwhile, the convergence of the RL-rNMPC algorithm and the admissibility of Nash equilibrium strategies are comprehensively analyzed. Afterwards, the specific implementation process of the RL-rNMPC algorithm is elaborated to facilitate replicability. Finally, the simulation experiments demonstrate that the RL-rNMPC algorithm exhibits good control performance and robustness when facing complex systems with disturbances. Compared with other algorithms, the established algorithm also has better progressiveness.</p>

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Reinforcement learning-based robust model predictive control for nonlinear zero-sum games

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Peng Xin,
  • Ding Wang,
  • Ao Liu,
  • Junfei Qiao

摘要

In this article, a robust model predictive control (MPC) approach based on reinforcement learning (RL) techniques and adaptive critic designs is established to address zero-sum game problems of complex systems with disturbances. During the real-time interaction between the environment and the agent, a formidable challenge is posed for maintaining the stable operation of systems due to the disturbances caused by the environment, which is regarded as a two-player zero-sum game problem of nonlinear MPC (NMPC) in this article. According to the intelligent critic mechanism, the RL-based robust NMPC (RL-rNMPC) framework is first constructed to resolve the Nash equilibrium strategies. It is worth mentioning that the relaxed iteration scheme is introduced to expedite the iteration process within each prediction horizon. Meanwhile, the convergence of the RL-rNMPC algorithm and the admissibility of Nash equilibrium strategies are comprehensively analyzed. Afterwards, the specific implementation process of the RL-rNMPC algorithm is elaborated to facilitate replicability. Finally, the simulation experiments demonstrate that the RL-rNMPC algorithm exhibits good control performance and robustness when facing complex systems with disturbances. Compared with other algorithms, the established algorithm also has better progressiveness.