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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.