Adaptive Tracking Control Schemes for Fuzzy Approximation-Based Noncanonical Nonlinear Systems with Hysteresis Inputs

In this paper, the tracking control problem of a class of fuzzy approximation-based noncanonical nonlinear systems with hysteresis inputs is investigated, where the fuzzy weight matrix is not available for measurement, and the hysteresis nonlinearities are modeled by the Prandtl–Ishlinskii operator. Due to the coupling effects, the plant input containing hysteresis is unknown. To solve the problem, two adaptive control schemes are developed. The first is a Lyapunov-based scheme, and the second is a gradient-based scheme. For convenience, only the relative-degree-one case is taken into account in design and analysis. With the proposed schemes, it can be proved that all signals in the closed-loop system are bounded, and the tracking error converges to a small region around zero. Simulation results show that the maximum steady-state error converges to [−0.0131,0.0183]μm and [−0.0139,0.0161]μm with two control schemes, which confirms the obtained results.