Type ۲ Neuro-Fuzzy Controller for a Class of Delayed Nonlinear Systems

This article explores the design of a type ۲ neuro-fuzzy controller specifically for managing delayed nonlinear systems through feedback error training. The feedback error training framework incorporates a traditional controller in the feedback loop to stabilize the system. Meanwhile, the forward loop employs a type ۲ neuro-fuzzy controller, which serves as an intelligent controller to address system nonlinearity and time delay issues. The parameters of the type ۲ neuro-fuzzy controller are fine-tuned using the gradient descent method within this framework. To assess the stability of both the closed-loop system and the parameter adjustment algorithm, a Lyapunov-Krasowski function is utilized. This function demonstrates that the tracking error can be reduced to zero, even with the presence of delay in the control system input. Furthermore, the regulation rules for the intelligent controller's parameters can be derived without needing the exact mathematical model or parameters of the system being controlled, thus simplifying the calculations. The proposed method has been applied to control an inverse pendulum system characterized by nonlinear behavior and time-varying delays in its input due to network-based control. Additionally, sensor measurements are assumed to be noisy. Simulation results validate the effectiveness of the designed controller across various time delay scenarios and noise levels.

کلیدواژه ها:

Delayed Nonlinear Systems ، Type ۲ Neuro-Fuzzy Controller ، Lyapunov-Krasovski Function ، Measurement Noise ، Stability