Adaptive variable universe of discourse fuzzy control for a class of nonlinear systems with unknown dead zones

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single-input-single-output strict-feedback nonlinear systems with unknown dead-zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state-feedback control is changed to output-feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping-based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction-expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed-loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach.