Behavioral Analysis of an Interval Type-2 Fuzzy Controller Designed with Harmony Search Enhanced with Shadowed Type-2 Fuzzy Parameter Adaptation

The challenges we face in today's world are increasingly complex, and effectively managing uncertainty when modeling control problems can yield significant benefits. However, the complexity of these models often leads to higher computational costs. Therefore, the main contribution of this article is the use of the theory of shadowed type-2 fuzzy sets to address these challenges and to control the search space exploration in the harmony search algorithm by employing two alpha planes, and with this, it was possible to reduce the computational cost and obtain effective results. Furthermore, the application of this approach aims to find optimal parameters for the membership functions of a type-2 fuzzy controller and analyze its behavior. By adopting the proposed methodology, it becomes possible to minimize computational costs while still achieving feasible solutions for interval type-2 control problems. A key aspect is that symmetry is considered in the design of the controller to also obtain good results. To validate the effectiveness of the approach, extensive simulations were conducted with varying levels of noise introduced to the type-2 controller. This comprehensive analysis allowed for a thorough examination of the results obtained. The findings of the simulations are presented, showcasing the advantages of the proposed methodology. By incorporating noise into the system, it was observed that the objective function, in this case, the root mean square error (RMSE), was reduced. Moreover, the signal obtained with the presence of noise demonstrated a superior performance compared to the noise-free reference. In conclusion, the proposed approach of utilizing shadowed type-2 fuzzy systems, combined with the harmony search algorithm, offers a promising solution for managing complex control problems. By carefully analyzing the behavior of the system through simulations, it is evident that the inclusion of noise helps improve the system's performance.