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<p>This paper proposes a novel model-free inverse optimal control (IOC) method for general nonlinear continuous-time systems based on <i>Q</i>-learning, which overcomes the limitations of existing approaches that rely on affine system structures and explicit model information. First, an inner-outer two-layer iterative framework is designed, where the inner layer approximates the optimal control policy and <i>Q</i>-function, while the outer layer identifies the cost function parameters from expert trajectories. Then, for the first time, a rigorous theoretical convergence analysis of the <i>Q</i>-learning algorithm for continuous-time nonlinear systems is provided. And the policy reconstruction and cost function inference are achieved using only expert data. The paper also employs neural networks to construct an actor-critic architecture and updates weights via gradient-based optimization. Finally, numerical simulations are conducted to verify the effectiveness of the proposed algorithm, offering new theoretical foundations and technical pathways for inverse optimal control of nonlinear systems.</p>

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Inverse optimal control of general nonlinear systems based on adaptive dynamic programming

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Mei Li,
  • Zhongyang Ming,
  • Weizhao Song,
  • Jiayue Sun

摘要

This paper proposes a novel model-free inverse optimal control (IOC) method for general nonlinear continuous-time systems based on Q-learning, which overcomes the limitations of existing approaches that rely on affine system structures and explicit model information. First, an inner-outer two-layer iterative framework is designed, where the inner layer approximates the optimal control policy and Q-function, while the outer layer identifies the cost function parameters from expert trajectories. Then, for the first time, a rigorous theoretical convergence analysis of the Q-learning algorithm for continuous-time nonlinear systems is provided. And the policy reconstruction and cost function inference are achieved using only expert data. The paper also employs neural networks to construct an actor-critic architecture and updates weights via gradient-based optimization. Finally, numerical simulations are conducted to verify the effectiveness of the proposed algorithm, offering new theoretical foundations and technical pathways for inverse optimal control of nonlinear systems.