Nonlinear Filters-Based Adaptive Fuzzy Control of Strict-Feedback Nonlinear Systems With Unknown Asymmetric Dead-Zone Output

This paper presents a nonlinear filters-based adap-tive fuzzy control design for strict-feedback nonlinear systems with unknown asymmetric dead-zone output and virtual con-trol coefficients. First, a novel smooth approximation of the non-smooth asymmetric output dead-zone nonlinearity is con-structed to improve the approximation performance and speed. Then, to dilute the effects of unknown dead-zone and vir-tual control coefficients, an adaptive compensation mechanism is presented by utilizing projection operators techniques and the properties of fuzzy basis functions and hyperbolic tangent functions. Further, a novel adaptive backstepping control design method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also completely compensates the effects of the boundary errors generated by the introduced filters in spite of unknown virtual control coefficients. From the properties of the smooth projection operator, and based on Lyapunov synthesis, it is shown that all closed-loop signals are ensured uniformly bounded. Finally, the applicability of the proposed control method is rigorously verified by a example of one-link manipulator with a brushed dc motor.