Focusing on the nonlinear time-delay systems actuated by smart-material-based actuators, an adaptive dynamic surface estimated inverse motion control scheme is proposed in this article. The asymmetric hysteresis nonlinearity is counteracted by constructing its evaluated inverse compensator. A state estimator is constructed to estimate the unmeasurable states and at the same time to cope with external disturbances. The assumptions on time-delay functions are removed, and the unknown time-delay function is online evaluated by combining the fuzzy logic system with a finite covering lemma. Also, the prespecified tracking performance is achieved by utilizing an error-transformed function. Experimental results of the proposed controller are performed on the piezoelectric positioning stage to verify the effectiveness of the control scheme.
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