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A stabilized optimal control (SOC) scheme for Hammerstein system with backlash is proposed in this paper. A concise expression of the non-smooth nonlinear link in the dynamic system is derived by introducing several switching functions. Then, to deal with the model mismatch problem, a model error compensator (MEC) is also introduced. Subsequently, by minimizing the defined objective function integrating with stability analysis, the stabilized optimal control strategy is proposed. Finally, the results of simulation based on the background of mechanical transmission are presented.
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Wang et al. (2023) studied this question.