A hybrid Fuzzy neural network approach for nonlinear control systems: Performance, adaptability, and robustness

This study presents a Fuzzy Neural Network (FNN)-based control architecture for nonlinear control mapping and evaluates its performance using a stable second-order benchmark plant. The proposed FNN combines a compact seven-rule fuzzy structure with a hybrid AND/OR inference mechanism and a hybrid learning strategy based on Least Squares Estimation (LSE) and Gradient Descent (GD). Five operating-condition variables are used as fuzzy inputs, while Gaussian membership functions represent the antecedent variables. LSE is employed to estimate the consequent parameters, whereas GD is used to adapt the antecedent membership-function parameters during offline training. The proposed controller is compared with classical PID and conventional Fuzzy controllers, as well as Adaptive Neuro-Fuzzy Inference System (ANFIS), Takagi-Sugeno (TSK), and Interval Type-2 Fuzzy (IT2Fuzzy) controllers under common benchmark simulation conditions. The evaluation considers transient response, gain variations, external disturbances, measurement noise, and parameter perturbations. Under the reported nominal step-response comparison, the proposed FNN achieves a rise time of 0.72 s, a settling time of 1.28 s, and zero measured overshoot. The IT2-Fuzzy controller achieves an overshoot of 4.03%, whereas PID, conventional Fuzzy, ANFIS, and TSK exhibit overshoots of 16.30%, 12.63%, 14.77%, and 9.48%, respectively. Sensitivity and noise analyses further indicate that the proposed seven-rule architecture maintains favorable performance under the investigated parameter variations and measurement-noise conditions. The results demonstrate that the proposed FNN provides a compact and interpretable framework for nonlinear control mapping, offering favorable transient performance with limited rule complexity. Since the evaluation is based on numerical simulations, experimental validation on physical control platforms is required to further assess its practical applicability.