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<p>In this article, the authors investigate and derive adaptive strategies for the pursuit-evasion problem where both players lack knowledge of the opponent’s cost function parameters, which has rarely been investigated in the existing literature. To address this challenge, the authors consider a basic information structure that assumes that the evader will use an adaptive learning algorithm to estimate the unknown parameters and update its adaptive strategy piecewise, whereas the pursuer will adopt a strategy based on the opponent’s choices at each time instant. By employing methods of diminishing excitation and random switching, the authors establish certain excitation conditions for signals of the closed-loop game system to ensure the strong consistency of the parameter estimates. Moreover, the authors demonstrate that the adaptive game system can asymptotically reach the Nash equilibrium, which is the same equilibrium achieved in pursuit-evasion games when all game parameters are known.</p>

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Adaptive Pursuit-Evasion Differential Game with Unknown Cost Functions

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Zhixing Chen,
  • Lei Guo

摘要

In this article, the authors investigate and derive adaptive strategies for the pursuit-evasion problem where both players lack knowledge of the opponent’s cost function parameters, which has rarely been investigated in the existing literature. To address this challenge, the authors consider a basic information structure that assumes that the evader will use an adaptive learning algorithm to estimate the unknown parameters and update its adaptive strategy piecewise, whereas the pursuer will adopt a strategy based on the opponent’s choices at each time instant. By employing methods of diminishing excitation and random switching, the authors establish certain excitation conditions for signals of the closed-loop game system to ensure the strong consistency of the parameter estimates. Moreover, the authors demonstrate that the adaptive game system can asymptotically reach the Nash equilibrium, which is the same equilibrium achieved in pursuit-evasion games when all game parameters are known.