A Survey of Adaptive Fuzzy Controllers: Nonlinearities and Classifications

Adaptive fuzzy controllers (AFCs), i.e., fuzzy controllers using heuristic expert knowledge and equipped with adaption ability, are widely used in the industry in the present days as they are capable of dealing with ill-formulated nonlinear systems (where exact mathematical formulas are not known) or partially described nonlinear systems. AFCs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities. Over the last two decades, many different approaches toward adaptive fuzzy control have been reported. In this paper, we recapitulate the latest research works related to AFCs and provide an up-to-date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled. We categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems, nonlinear systems with external disturbances, nonlinear systems with some special type of nonlinearities, nonaffine nonlinear systems, and strict-feedback nonlinear systems. It turns out that many existing methods are subject to various limitations, and none of them is capable of controlling a general nonlinear systems. Hence, it is still an open problem to design and develop a universal AFC for a general class of nonlinear systems.

I. Introduction

Fuzzy controllers are nonlinear controllers designed using fuzzy logic. Fuzzy sets were first introduced by Zadeh in 1965 in [1]. Furthermore, fuzzy sets have been used to represent linguistic information, following which fuzzy systems (FSs) have been evolved to a new type of controller known as fuzzy controller. Fuzzy controllers have been incorporated in different applications like railways, washing machines, air conditioners, autofocusing cameras, robots, automobiles, and many more. Fuzzy logic systems equipped with a training algorithm [2] are termed adaptive FSs [3] , [4]. The corresponding controller known as adaptive fuzzy controller (AFC) has been used to deal with different nonlinearities. When there is no appropriate mathematical model of a physical system or when there is lack of proper information (may be only linguistic information is available), a conventional controller or an adaptive conventional controller does not help to control the physical system. In this context, an AFC plays a pivotal role in controlling the system because it is able to use available linguistic information. More about AFCs will be discussed in the following.