| Title | Type-2 Fuzzy Control vs Type-1 Fuzzy Control: An Analytical Perspective |
| Speaker | Prof. Hao Ying |
| Chair | Sundaram Suresh |
Abstract
Control systems involving type-2 (T2) fuzzy sets and fuzzy logic (i.e., T2 fuzzy control) are drawing increasing attention while the highly successful type-1 (T1) fuzzy control is maturing with over 35 years of theoretical research results and countless numbers of real-world applications around the globe. The number of reports is relatively small at present, but there is an upward trend. The membership function of a T2 fuzzy set is three-dimensional whereas that of a T1 fuzzy set is two dimensional. The new third dimension membership function enables the T2 fuzzy set to characterize the membership function uncertainties in a quantitative manner. Using the T2 fuzzy control results from their applications, experiments, and simulations, some authors have claimed in literature that the T2 fuzzy controllers can outperform the T1 fuzzy controllers in terms of control performance. Theoretical exploration in this regard is necessary because experiment-based observations have inherent limitations – they cannot be comprehensive and can even sometimes be incorrect. Such theoretical development, however, is still in its infancy.
A T2 fuzzy controller, like its T1 counterparts, is currently viewed and treated by many fuzzy control practitioners and researchers as a black box that is a function generator which produces a desired nonlinear mapping between input and output of the controller (we call the mapping an analytical structure). The analytical structure’s implicit mathematical representation linking the output variable u with the input variable vector x, u = f(x), is the nonlinear control solution being sought. In this presentation, we will demonstrate the latest new techniques capable of deriving the explicit mathematical representation of f(x) for some common interval T2 fuzzy controllers. Connections between the resulting analytical structures and the conventional nonlinear controllers (e.g., the PID controller) will be shown and insightful analyses will be provided. f(x) of the T2 fuzzy controllers will be compared with those of the comparable T1 fuzzy controllers and their relative advantages and disadvantages will be exposed. We will not only cover control performance but system complexities as well (e.g., the number of design parameters), as the latter alone often determines the fate of a controller in real-world applications.
Biography
Dr. Hao Ying is a Professor at the Department of Electrical and Computer Engineering, Wayne State University, Detroit, USA. As sole author, he published the book entitled Fuzzy Control and Modeling: Analytical Foundations and Applications (IEEE Press, 2000), and co-authors the book Type-2 Fuzzy Logic Control: Introduction to Theory and Applications (John Wiley & Sons, Inc., 2013). In addition, he has published more than 90 peer-reviewed journal papers and over 140 conference papers. He is a Fellow of IEEE.