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

This paper presents a nonlinear filters-based adaptive fuzzy control design for strict-feedback nonlinear systems with unknown asymmetric dead-zone output and virtual control coefficients. First, a novel smooth approximation of the non-smooth asymmetric output dead-zone nonlinearity is constructed to improve the approximation performance and speed. Then, to dilute the effects of unknown dead-zone and virtual 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.
Note to Practitioners
—Strict-feedback nonlinear systems can be utilized to model many practical engineering systems, such as one-link manipulator, permanent magnet synchronous motor, robots with flexible joints, spacecrafts, etc. Due to the physical limitations and other factors, non-smooth dead-zone nonlinearity often presents in system components, which will influence the control performance and threat the operation security. Therefore, this paper considers the control design problem for strict-feedback nonlinear systems with unknown asymmetric dead-zone output nonlinearity, and the proposed control algorithm is successfully applied to one-link manipulator with a brushed dc motor. In addition, the virtual control coefficients are often assumed to be known constants or known nonlinear functions with known bounds in the existing results, which is unrealistic on account of the economic costs and environmental factors. To erase such limitation, this paper presents a novel adaptive compensation mechanism based on smooth auxiliary function dependent on the property of tanh-function and the projection operator technique.