The issue of observer-based adaptive sliding mode control of nonlinear Takagi–Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an ${H}_{\infty }$ performance disturbance attenuation level ${\gamma }$ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

中文翻译：

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带有不可估计前提变量的非线性半马尔可夫跳跃TS模糊系统的滑模观测器自适应控制

研究了具有半马尔可夫切换和不可测前提变量的非线性Takagi-Sugeno模糊系统的基于观测器的自适应滑模控制问题。由于前提变量的选择是系统的状态，因此在模型中描述了更通用的非线性系统。首先，在观察者空间上提出了一种新的积分滑动面函数，然后根据估计的前提变量获得了滑模动力学和误差动力学。第二，具有随机稳定性的充分条件 $ {H} _ {\ infty} $ 性能扰动衰减水平 $ {\ gamma} $ 基于通常不确定的跃迁速率，可以得到具有不同输入矩阵的滑模动力学。第三，基于观察者的自适应控制器被合成以确保预定义滑动表面的有限时间可达性。最后，提供了单链接机器人手臂模型以数字方式验证控制方案。