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 unknown feedback linearizable nonlinear dynamical systems using a discrete-time fuzzy logic controller (FLC). Discrete-time FLC design is significant because almost all FLCs are implemented on digital computers. A repeatable design algorithm and a stability proof for an adaptive fuzzy logic controller is presented that uses basis functions based on the fuzzy system, unlike most standard adaptive control approaches which generate basis vectors by computing a ''regression matrix''. A new approach to adapt the fuzzy system parameters is attempted. With mild assumptions on the class of discrete-time nonlinear systems, using this adaptive fuzzy logic controller the uniform ultimate boundedness of the closed-loop signals is shown under a persistency of excitation (PE) condition. New passivity properties of fuzzy logic systems are described. The result is a model-free universal fuzzy controller that works for any system in the given class of systems.