Type-3 Fuzzy Dynamic Adaptation of the Crossover Parameter in Differential Evolution for the Optimal Design of Type-3 Fuzzy Controllers for the Inverted Pendulum

This paper proposes a dynamic adaptation of the crossover parameter (CR) in Differential Evolution (DE) using Type-3 fuzzy logic. The strategy involves adjusting the CR value according to the progress of the algorithm by employing a Type-3 fuzzy system (T3FS) to handle the uncertainty and variability inherent in this parameter. To assess the effectiveness of the proposed approach, an inverted pendulum system controlled by a T3FS is employed. The controller parameters are optimized using an enhanced DE algorithm. The results demonstrate that dynamically adapting the crossover rate parameter significantly enhances both the efficiency and accuracy of the DE algorithm, compared to traditional static adjustments. Specifically, the proposed approach achieved an RMSE of 0.0127, outperforming traditional static adjustment methods, which resulted in an RMSE of 0.732. In addition, the results exhibit an improvement in the consistency of the outcomes, with a significantly lower standard deviation (0.0111) compared to conventional methods. These findings underscore the potential of Type-3 fuzzy systems (T3FSs) in enhancing evolutionary algorithms for optimizing fuzzy controllers in highly uncertain nonlinear systems. Furthermore, this emphasizes the capability of T3FSs to enhance evolutionary algorithms in optimizing fuzzy controllers for nonlinear systems subject to significant uncertainty.