This paper discusses the adaptive control for the uncertain discrete time linear systems preceded by hysteresis nonlinearity described by the Prandtl-Ishlinskii (PI) model. The contribution of the paper is the development of an adaptive algorithm in which a pseudo-inversion is introduced to avoid difficulties of the directly inverse construction for complex hysteresis models, especially for the unknown hysteresis case. In the developed approach, only those parameters in the formulation of the sliding mode controller are adaptively estimated. The stability in the sense that all signals in the loop remain bounded is analyzed. Simulation results show the effectiveness of the proposed algorithm.
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