Robust Adaptive Control of State-Constrained Hysteretic Nonlinear Systems via Fuzzy Pseudoinverse Compensation: Application to Giant Magnetostrictive Actuators

This article proposes a robust adaptive fuzzy pseudoinverse control strategy for hysteretic nonlinear systems subject to strict state constraints, specifically targeting giant magnetostrictive actuators (GMA). To address physical constraints and uncertain control gains, an improved integral barrier Lyapunov function (IBLF) is employed, enabling direct enforcement of state constraints without feasibility condition verification. Furthermore, a command-filtered backstepping framework combined with a fixed-time compensation mechanism is developed. This approach not only circumvents the explosion of complexity inherent in traditional backstepping but also effectively attenuates filtering errors to enhance robustness. To mitigate severe hysteresis nonlinearity, a fuzzy pseudoinverse control scheme is constructed to compensate for hysteresis effects without requiring an explicit inverse model. Comprehensive experimental validations on a GMA platform—covering single-frequency, composite-frequency, square wave, and triangular wave trajectory tracking—demonstrate the superiority of the proposed method. Experimental results confirm that the strategy achieves high-precision motion control with minimal tracking error and strictly satisfies system constraints under various dynamic conditions.