Adaptive fuzzy logic control of discrete-time dynamical systems

This paper demonstrates tracking control of a class of unknown nonlinear dynamical systems using a discrete-time fuzzy logic controller (FLC). Designing a discrete-time FLC is significant because almost all FLCs are implemented on digital computers. A repeatable design algorithm and a stability proof are presented for an adaptive fuzzy logic controller that uses basis vectors based on the fuzzy system, unlike most standard adaptive control approaches which use basis vectors depending on the unknown plant (e.g. a tediously computed "regression matrix"). The authors select an e-modification sort of approach to adapt the fuzzy system parameters. Using this adaptive fuzzy logic controller, the authors prove uniform ultimate boundedness of the closed-loop signals and that the controller achieves tracking. In fact, the fuzzy system designed is a model-free universal fuzzy controller that works for any system in the given class of systems.