Robust stabilization of fractional spatiotemporal chaos via model-free deep reinforcement learning.

Abstract

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 (α=1.85), exhibits universal robustness across the regime α∈[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.