Model reference fuzzy adaptive control for uncertain dynamical systems with time delays

This paper investigates a model reference fuzzy adaptive control (MRFAC) scheme for uncertain dynamical systems with known structures but unknown parameters which are dependent on known variables, multiple delayed state uncertain ties, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A fuzzy basis function expansion (FBFE) is used to represent the unknown parameters of the controlled system from the strategic manipulation of the model following tracking errors. The proposed MRFAC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FBFE simultaneously. Stability and robustness of the MRFAC scheme is analyzed in the sense of Lyapunov. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with the model following tracking errors uniformly ultimately bounded in the presence of plant parameter uncertainties, delayed state uncertainties, and external disturbances. The theoretical results are evaluated through a gyroscopic system with a single actuating input.