Adaptive fuzzy logic control of feedback linearizable discrete-time dynamical systems under persistence of excitation

The objective of this paper is to achieve,tracking control of a class of un known feedback linearizable nonlinear dynamical systems using a discrete-ti me fuzzy logic controller (FLC). Discrete-time FLC design is significant be cause almost all FLCs are implemented on digital computers. A repeatable de sign algorithm and a stability proof for an adaptive fuzzy logic controller is presented that uses basis functions based on the fuzzy system, unlike m ost standard adaptive control approaches which generate basis vectors by co mputing a "regression matrix". A new approach to adapt the fuzzy system par ameters is attempted. With mild assumptions on the class of discrete-time n onlinear systems, using this adaptive fuzzy logic controller the uniform ul timate boundedness of the closed-loop signals is shown under a persistency of excitation (PE) condition. New passivity properties of fuzzy logic syste ms are described. The result is a model-free universal fuzzy controller tha t works for any system in the given class of systems. (C) 1998 Elsevier Sci ence Ltd. All rights reserved.