To address the Multi-agent Visibility-based Persistent Monitoring (MVPM) problem using clustered unmanned systems, we propose an enhanced Q-value mixing network named KAN-Mix, which incorporates Kolmogorov–Arnold networks. Additionally, we design the MVPM reward based on information entropy, introducing information dynamics and probability theory into the framework. Comprehensive experiments validate the performance of KAN-Mix, demonstrating significant improvements in both coverage rate and intruder detection rate compared to the original QMIX method. Our algorithm demonstrates a performance improvement of 6–12.3% in the coverage rate of maps compared to the QMIX algorithm across three distinct maps. Additionally, it exhibits a significantly higher catch rate than both learning-based and traditional algorithms, with some maps achieving success rates of up to 100%. The average number of catch steps required to capture intruders ranks among the top two on all maps. The entropy-based reward outperforms the traditional coverage-based reward by 6.4–58.3% in coverage and by 6–61.9% in the number of catch steps. The entropy-based reward is shown to be more effective than the traditional coverage-based rewards. Combining these advantages, KAN-Mix delivers superior results compared to all standard Q-value strategies.