Adaptive fuzzy logic control of feedback linearizable discrete-time nonlinear systems

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 the 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 novel approach to adapt the fuzzy system parameters is attempted. Using this adaptive fuzzy logic controller, with mild assumptions on the class of discrete-time nonlinear systems, the uniform ultimate boundedness of the closed-loop signals is presented. Certainty equivalence is not used and regression matrix not required. The result is a model-free universal fuzzy controller that works for any system in the given class of systems.