In this paper, the problem of adaptive sliding mode control for varied one-sided Lipschitz nonlinear systems with uncertainties is investigated. In contrast to existing sliding mode control design methods, the considered models, in the current study, are affected by nonlinear control inputs, one-sided Lipschitz nonlinearities, unknown disturbances and parameter uncertainties. At first, to design the sliding surface, a specific switching function is defined. The corresponding nonlinear equivalent control is extracted and the resulting sliding mode dynamic is given. Novel synthesis conditions of asymptotic stability are derived in terms of linear matrix inequalities. Thereafter, to ensure the reachability of system states and the occurrence of the sliding mode, the sliding mode controller is designed. Any knowledge of the upper bound on the perturbation is not required and an adaptation law is proposed. At last, two illustrative examples are introduced.

中文翻译：

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通过自适应滑模控制实现单侧Lipschitz非线性系统的鲁棒镇定

本文研究了具有不确定性的变化单侧Lipschitz非线性系统的自适应滑模控制问题。与现有的滑模控制设计方法相比，当前研究中考虑的模型受非线性控制输入，单侧Lipschitz非线性，未知干扰和参数不确定性的影响。首先，为了设计滑动表面，定义了特定的开关功能。提取相应的非线性等效控制，并给出所得的滑模动力学。根据线性矩阵不等式推导了渐近稳定性的新合成条件。此后，为了确保系统状态的可达性和出现滑模，设计了滑模控制器。不需要任何关于扰动的上限的知识，并且提出了适应定律。最后，介绍了两个示例。