The fractional Kuramoto-Sivashinsky equation (F-KSE) describes a class of spatiotemporal chaotic systems characterized by nonlocal dissipative interactions. Controlling such systems presents significant challenges due to the interplay between nonlinear convection and fractional diffusion. This study investigates a model-free feedback control framework to stabilize the F-KSE. By formulating the control problem as a high-dimensional optimization task, a continuous control law is derived without assuming prior knowledge of the governing equations. Numerical experiments demonstrate that the proposed controller effectively suppresses chaotic wave shedding, forcing the system into a near-trivial stationary state with an energy reduction consistently exceeding 96% (reaching a peak of 98.55% across the diffusive regime). Spectral analysis reveals that the stabilization is achieved through broadband suppression of dominant instability modes. Most notably, a sensitivity analysis demonstrates that a single control policy, trained at a specific fractional order ($\alpha =1.85$), exhibits universal robustness across the regime $\alpha \in [1.0,2.0]$ without retraining. This suggests the data-driven agent identifies a dominant stabilization mechanism that primarily counteracts energy-containing structures driven by the convective nonlinearity. The resulting policy is largely invariant to the underlying dissipative structure.

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• Anomalous diffusion
• Control & applications of chaos
• Flow control
• Fractional dimension
• Pattern formation
• Spatiotemporal chaos
• Turbulence control
• Kuramoto model
• Numerical techniques
• Reinforcement learning