Data-Driven Interval Type-2 Fuzzy Inference System Based on the Interval Type-2 Distending Function

Fuzzy type-2 modeling techniques are increasingly being used to model uncertain dynamical systems. However, some challenges arise when applying the existing techniques. These are the following: 1) a large number of rules are required to complete cover the whole input space; 2) a large number of parameters associated with type-2 membership functions have to be determined; 3) the identified fuzzy model is usually difficult to interpret due to the large number of rules; and 4) designing a fuzzy type-2 controller using these models is a computationally expensive task. To overcome these limitations, a procedure is proposed here to identify the fuzzy type-2 model directly from the data. This model is called the distending-function-based fuzzy inference system (DFIS). This model consists of rules and interval type-2 distending functions. First, a few key rules are identified from the data, and later, more rules are added until the error is less than the threshold. The proposed procedure is used to model the altitude controller of a quadcopter. The performance of the DFIS model is compared with that of various fuzzy models. Furthermore, a simplified procedure based on the rules is presented to design a computationally low-cost type-2 controller. The effectiveness of the controller is shown by regulating the height of a quadcopter in the presence of noisy sensory data. The performance of this controller is compared with that of various other controllers. Finally, the proposed type-2 controller was implemented on a Parrot Mambo quadcopter to demonstrate its real-time performance.