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<p>In this article, an advanced accelerated Q-learning (AQL) approach is designed to address the nonlinear discrete-time optimal tracking problem of zero-sum games with unknown dynamics. Different from conventional adaptive dynamic programming methods, the advanced Q-learning algorithm incorporates both the control input and the disturbance signal into the tracking error, which obviates the quadratic form of control and disturbance inputs directly. This innovative Q-function is used to derive the optimal tracking control policy pair that ensures the terminal tracking error asymptotically converges to zero, independent of the feedforward control input. In order to improve the convergence speed of the iterative process and reduce computational complexity, an accelerated factor is introduced. After collecting offline input–output data, a backpropagation neural network is employed to approximate the proposed Q-function, which enables model-free tracking control of zero-sum games through an off-policy learning mechanism. Furthermore, the theoretical properties of the developed algorithm are analyzed under specific preconditions. Finally, the effectiveness of the AQL algorithm is validated through a numerical simulation, which is implemented using a critic-only structure.</p>

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Model-free tracking design for nonlinear zero-sum games with an improved utility function

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Ding Wang,
  • Guohan Tang,
  • Jin Ren,
  • Mingming Zhao,
  • Junfei Qiao

摘要

In this article, an advanced accelerated Q-learning (AQL) approach is designed to address the nonlinear discrete-time optimal tracking problem of zero-sum games with unknown dynamics. Different from conventional adaptive dynamic programming methods, the advanced Q-learning algorithm incorporates both the control input and the disturbance signal into the tracking error, which obviates the quadratic form of control and disturbance inputs directly. This innovative Q-function is used to derive the optimal tracking control policy pair that ensures the terminal tracking error asymptotically converges to zero, independent of the feedforward control input. In order to improve the convergence speed of the iterative process and reduce computational complexity, an accelerated factor is introduced. After collecting offline input–output data, a backpropagation neural network is employed to approximate the proposed Q-function, which enables model-free tracking control of zero-sum games through an off-policy learning mechanism. Furthermore, the theoretical properties of the developed algorithm are analyzed under specific preconditions. Finally, the effectiveness of the AQL algorithm is validated through a numerical simulation, which is implemented using a critic-only structure.