Robust Distributed Resource Allocation Based on PID Control with Nabla Fractional Difference

In many real-world applications, resource allocation in the presence of disturbances poses significant challenges due to the dynamic and uncertain nature of the environment. Traditional optimization algorithms often struggle to maintain robustness and efficiency under these conditions. This paper addresses the resource allocation problem with disturbances by proposing a novel distributed optimization algorithm. The proposed algorithm integrates the principles of proportional- integral-derivative (PID) control, discrete sliding mode control, and nabla fractional difference, resulting in enhanced robustness, flexibility, and efficiency. Through extensive numerical simu-lations, the correctness and effectiveness of the algorithm are thoroughly validated, demonstrating its potential to outperform existing approaches in disturbed environments.