Stable Adaptive Control Using Fuzzy Systems and Neural Networks

Abstract

Fuzzy controllers have stirred a great deal of excitement in some circles since they allow for the simple inclusion of heuristic knowledge about how to control a plant rather than requiring exact mathematical models. This can sometimes lead to good controller designs in a very short period of time. In situations where heuristics do not provide enough information to specify all the parameters of the fuzzy controller a priori, researchers have introduced adaptive schemes that use data gathered during the on-line operation of the controller, and special adaptation heuristics, to automatically learn these parameters (see e.g. [1] – [12] or the References therein). To date, stability conditions have not been provided for any of the approaches in [1] – [12], but Langari and Tomizuka [13] and others have developed stability conditions for (non-adaptive) fuzzy controllers and recently several innovative stable adaptive fuzzy control schemes have been introduced [14] – [17]. Moreover, closely related neural control approaches have been studied [18] – [23]. In this article, we seek to introduce an adaptive fuzzy or neural control approach which is guaranteed to operate properly under less restrictive assumptions and for more general continuous-time nonlinear systems.