Time-varying fuzzy sets in adaptive control

This paper deal with the use of fuzzy sets whose shape evolves as the error to construct a robust PDC fuzzy controller for nonlinear system in continuous time described by the T-S fuzzy model. This controller is based on time-Varying Fuzzy Sets (VFS) characterized by the displacement of the support points to both right and left side of the universe of discourse, and they are directed by a well-defined criterion. This note focuses only on the displacement of the midpoint of the universe. The functions defining these displacements are determined by an adaptive temporal Lyapunov function depending on the error, that is the difference between desired and current system response evolves.