Adaptive asymptotic tracking control for multi-input and multi-output nonlinear systems with unknown hysteresis inputs

Abstract

With the advantages in resolution, response speed, and reliability, smart materials such as piezoelectric ceramics and shape memory alloys are widely used in modern industries, and the hysteresis phenomenon in such smart materials has also received extensive attention. The existing tracking control schemes for nonlinear systems with backlash-like hysteresis inputs may have singularity problems, and it is difficult to obtain a high-precision tracking effect. To resolve the above issues, a novel adaptive asymptotic tracking control strategy is proposed for multi-input and multi-output nonlinear systems with unknown backlash-like hysteresis inputs, where the dependence on the system model is removed through fuzzy logic systems and elaborately designed adaptive laws. In contrast, the proposed tracking control scheme is free of any singularity problem, and the constructed controllers and adaptive laws including positive and continuous functions with zero limit make the output tracking error asymptotically converge to zero rather than near the origin. Moreover, this asymptotic convergence is proven by rigorous theoretical analysis. Finally, the effectiveness and robustness of the proposed tracking control scheme are also verified by numerical and practical simulations.