Backstepping-based direct adaptive fuzzy control for SISO nonlinear systems

In this paper, adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear systems with lower triangular form. The backstepping technique is applied to construct an adaptive fuzzy tracking controller which guarantees the output of system to follow the reference signal, and ensures uniform ultimate boundedness of all signals in the closed-loop system. The tracking error dynamics are proved to converge to small neighborhood of the origin. The control performance of the closed -loop system is guaranteed by properly choosing the design parameters. The proposed scheme offers systematic design procedure for the control of the uncertain nonlinear systems with lower triangular form. A main advantage of the suggested design scheme is that the adaptive mechanism with minimal learning parameterizations is obtained. To solve tracking control problems for an n-th order nonlinear system, there are at most n parameters needed to be adapted online. Finally, two simulation examples are used to demonstrate the effectiveness of the approaches presented in this paper.