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] mu m and [-0.0139, 0.0161] mu m with two control schemes, which confirms the obtained results.