Adaptive fuzzy system-based variable-structure controller for multivariable nonaffine nonlinear uncertain systems subject to actuator nonlinearities

In this paper, a novel adaptive fuzzy variable-structure control approach is proposed for a class of multivariable nonaffine uncertain systems subject to dynamic nonlinear disturbances and actuator nonlinearities (dead zone and sector nonlinearities). By using the Taylor series expansion, an equivalent model in affine-like form is first derived for the nonaffine system. Then after, an adaptive fuzzy variable-structure controller is designed based on this affine-like equivalent model. The adaptive fuzzy systems are used to appropriately approximate the unknown nonlinear functions. The so-called SDU decomposition of the control gain matrix is exploited in the controller design and the stability analysis. It is proved that the proposed adaptive fuzzy control scheme can guarantee that all involved signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Finally, simulation results are presented to illustrate the effectiveness of this adaptive control system.