Developing a computationally effective Interval Type-2 TSK Fuzzy Logic Controller¹

Type-2 fuzzy logic controllers are capable of handling different types of uncertainties that naturally exist in most practical situations. However, the high computation cost of type-2 fuzzy logic controllers is a bottleneck for practically applying them to real-world applications. This paper introduces a novel approach for designing a computationally effective type-2 fuzzy logic controller. For this purpose, on the antecedent side, interval type-2 fuzzy sets are employed to capture the signal readings, which significantly reduce the computation costs while preserving the major advantages of general type-2 fuzzy logic systems. On the consequent side, however, the Takagi-Sugeno-Kang (TSK) technique is integrated with the proposed controller to render the control outputs in a parallel way. To further reduce the computation cost, the theory of uncertainty bounds is employed for the output processing of the proposed controller. To develop this control structure, a decomposition technique is integrated to break down the original type-2 fuzzy processes into type-1 and take advantage of type-1 fuzzy techniques, followed by an aggregation mechanism to calculate the collective output. The approach is applied to the control of an inverted pendulum and cart model. The simulation results of the developed interval type-2 fuzzy logic controller is compared with a type-1 TSK fuzzy logic controller and a classical proportional derivative (PD) controller. From the results, we have found a 16.6% and 23.3% improvement in Root Mean Square (RMS) error compared to type-1 TSK fuzzy logic controller and classical PD controller, respectively.