Deep neural network-based barrier function construction for pursuit–evasion games with capture radius

This paper addresses a two-dimensional pursuit–evasion game in a complex environment, explicitly incorporating a capture radius into the game formulation. The Evader aims to reach one of two designated target regions while avoiding capture, whereas the Pursuer’s objective is to intercept the Evader within its capture radius. As a preliminary step, the analytical barrier construction under the case of zero capture radius is first established, providing a theoretical baseline for subsequent extensions. The inclusion of a capture radius introduces significant nonlinearity into the reach–avoid boundary, making analytical solutions intractable, especially under complex spatial configurations. To overcome this challenge, a data-driven framework is proposed that employs a deep neural network, specifically a multilayer perceptron, to approximate the nonlinear barrier function from data generated via constrained optimization. The capture-radius-aware barrier surface separates the winning regions of the two players and accurately characterizes the Evader’s safe set under realistic geometric constraints. The proposed approach enables efficient estimation and visualization of the reach–avoid set. Finally, simulation experiments are conducted to validate both the accuracy and the geometric consistency of the neural approximation, showing that the predicted barriers align well with theoretical expectations.