This paper investigates an adaptive dynamic programming (ADP) optimal tracking control algorithm for multi-UAV systems based on zero-sum game theory, addressing external disturbances during flight. By formulating the bounded [Formula: see text] gain problem as a two-person zero-sum game between control strategies and external disturbances, the Hamilton-Jacobi-Isaacs (HJI) equation is constructed to derive the Nash equilibrium solution. To overcome the computational challenges of solving the HJI equation, a three-layer neural network structure comprising evaluation, execution, and disturbance networks is employed, integrated with the ADP algorithm to approximate the value function and optimize the control strategy iteratively. Comprehensive simulations demonstrate the proposed method's superior trajectory tracking performance and robustness compared to Sliding Mode Control (SMC). The results confirm the effectiveness of the ADP-based approach in achieving real-time, adaptive control in complex and dynamic multi-UAV environments.