Machine Learning-Based <i>L</i> ₁ Adaptive Control for a Class of Chaotic Systems

The stabilization of chaotic systems remains a critical research topic in control and systems theory, particularly due to the challenges introduced by model uncertainties. This study proposes a novel approach that integrates computational intelligence with the L₁ adaptive control framework to effectively address these challenges. Conventional L₁ adaptive control methods typically require accurate knowledge of specific parameters, which may be difficult or impractical to obtain. Furthermore, some parameters vary dynamically with system behavior, and treating them as constant can result in degraded performance. To overcome this limitation, a type-2 fuzzy neural network is employed to compute the low-pass filter parameters online and in real time. The stability of the proposed method is rigorously established through Lyapunov-based analysis. Simulation results demonstrate that the approach achieves effective and robust stabilization of chaotic systems under uncertain conditions.