Sigma adaptive fuzzy sliding mode control of a class of nonlinear systems

Based on fuzzy approximators of nonlinear functions, a new adaptive fuzzy s liding mode control scheme is proposed for a class of nonlinear plants. In comparison with most existing methods, in which the parameter projection al gorithm is often involved to prevent the estimated value of the input gain function from evolving into zero, the proposed control law has shown its su ccess and simplicity in tackling the case when the value of the estimated i nput gain function becomes zero during online operations. A variant of adap tive law with dead-zone sigma-modification is introduced to help achieve th is goal. The bounding parameters of the model approximation error and the e xternal disturbance are all regarded as unknown constants in this paper, an d adaptive laws for them are devised for tracking purposes. Based on Lyapun ov's stability theory the proposed controller has been shown to render the tracking error arbitrarily close to zero. A comparably good tracking perfor mance is obtained as illustrated by the simulation results for an inverted pendulum system.