This paper is concerned with the optimal guaranteed cost sliding-mode control problem for interval type-2 (IT2) Takagi–Sugeno fuzzy systems with time-varying delays and exogenous disturbances. In the presence of the uncertain parameters hidden in membership functions, an adaptive method is presented to handle the time-varying weight coefficients reflecting the change of the uncertain parameters. A new integral sliding surface is presented based on the system output. By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system. Optimal conditions of an $\mathcal {H}_{2}$ guaranteed cost function and an $\mathcal {H}_{\infty }$ performance index are established for the resulting time-delay control system. Finally, an inverted pendulum system represented by the IT2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme.

中文翻译：

---

区间2型模糊时滞系统的最优保本滑模控制

本文涉及具有时变延迟和外生扰动的区间类型 2 (IT2) Takagi-Sugeno 模糊系统的最优保证成本滑模控制问题。针对隶属函数中存在隐含的不确定参数，提出了一种自适应方法来处理反映不确定参数变化的时变权重系数。基于系统输出提出了一个新的积分滑动面。通过设计一种新颖的自适应滑模控制器，可以补偿系统扰动或建模误差，以闭环系统的最终一致有界性来保证滑动面的可达性。的最佳条件$\mathcal {H}_{2}$ 保证成本函数和 $\mathcal {H}_{\infty }$为由此产生的时延控制系统建立了性能指标。最后，应用以 IT2 模糊模型为代表的倒立摆系统来说明所提出的控制方案的优点和有效性。