Fuzzy control of discrete nonlinear systems with backlash

For a class of nonlinear discrete-time systems with input backlash, the fuzzy backlash model is used to replace the backlash inverse model, and the fuzzy backlash model is approximated by the linear combination of linear term and disturbance like term. The internal unknown function and external unknown disturbance of the closed-loop system are defined as the total disturbance of the system, and the discrete-time high-order sliding mode differentiator is used as the precise disturbance observer, and the total disturbance was controlled by an adaptive controller. Finally, Lyapunov theorem is used to prove the stability of the controller, and a simulation example is used to verify the feasibility of the scheme.