This paper aims to develop a state estimate-based friction fuzzy modeling and robust adaptive control techniques for controlling a class of multiple degrees of freedom (MDOF) mechanical systems. A fuzzy state estimator is proposed to estimate the state variables for friction modeling. Under some conditions, it is shown that such a state estimator guarantees the uniformly ultimate boundedness (UUB) of the estimate error. Based on system input–output data and our proposed state estimator, a robust adaptive fuzzy output-feedback control scheme is presented to control multiple degrees of freedom system with friction. The adaptive fuzzy output-feedback controller can guarantee the uniformly ultimate boundedness of the tracking error of the closed-loop system. A typical mass-spring system is employed in our simulation studies. The results demonstrate that our proposed techniques in this paper have good potential in controlling nonlinear systems with uncertain friction.

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