Backstepping-Based Finite-Time Adaptive Fuzzy Control of Unknown Nonlinear Systems

This paper proposes a backstepping-based finite-time adaptive fuzzy controller (BFAFC) for a nonlinear system in the present of unknown and uncertainty terms. A nonsingleton type-2 fuzzy system is presented to online approximate the unknown term in the nonlinear system, where the ellipsoidal type-2 membership functions are considered to deal with large amounts of uncertainties. Moreover, to further improve the control performance, the parameter adaptive laws are designed by the Lyapunov function and finite-time stability theorem in this paper such that not only the system stability but also the finite-time convergence can be guaranteed. Finally, the proposed BFAFC system is applied to an inverted pendulum and a coupled chaotic system to validate the effectiveness of the BFAFC system. Simulation results show that the proposed BFAFC system can cause the tracking error to converge to zero in a finite time and the tracking accuracy can be improved satisfactorily.