Control of unknown affine nonlinear systems with symmetric dead-zone

A control method based on adaptive fuzzy approximation is proposed in this paper to realize the tracking control problem for a class of symmetric dead-zone nonlinear systems. By decomposing the dynamics of dead-zone, a control law is derived by imbedding fuzzy approximators into backstepping steps. The proposed method is applicable to high-order nonlinear systems, and the controlled systems are not required to satisfy the matching conditions. The adopted fuzzy approximators are nonlinearly parameterized, which do not require fuzzy basis functions completely known. In order to obtain the adaptive laws, Taylor series expansion is employed to separate the nonlinear unknown parameters. And then the adaptive laws are designed on the basis of Lyapunov Stability. Besides, the adaptive laws are designed to adjust the norm of the unknown parameters, which can reduce the on-line computation burden and improve the control speed. It is proved that all closed-loop signals are guaranteed to converge to a small neighborhood of origin, and the output can track the reference signal with a given precision. An example is given to show the effectiveness of the method.