Predictor-Based Exponential Tracking of Turbulent Solutions for the Kuramoto--Sivashinsky Equation with Input Delay
The paper developed a predictor-backstepping control strategy to achieve uniform exponential tracking for turbulent solutions of the Kuramoto–Sivashinsky equation when subjected to constant input delay. The method successfully compensates for temporal mismatches by using a nonlinear predictor transformation, proving that the system remains globally well-posed and exhibits uniform exponential stability regardless of the initial time or reference trajectory.