PSO-Based Fractional-Order PID Control for Stabilizing the Chaotic Lorenz-84 Atmosphere Model

This study presents a novel control approach for stabilizing the chaotic behavior of the threedimensionalfractional-order Lorenz-84 atmosphere model. By leveraging the Grünwald–Letnikov discretization method, the fractional dynamics of the system are accurately modeled. A fractional-order proportional–integral–derivative (FOPID) controller is designed, with its parameters optimally tuned using Particle Swarm Optimization (PSO). The controller adapts the input signals based on real-time state-space feedback, enabling efficient suppression of chaotic oscillations. Numerical simulations demonstrate theeffectiveness of the PSO-tuned FOPID controller in achieving precise trajectory tracking and robust stabilization. The proposed method offers a promising solution for controlling fractional-order chaotic systems in atmospheric and other nonlinear contexts.