This paper proves the ultimately boundedness analysis for the trajectory tracking problem between the states of an uncertain nonlinear system represented by a Takagi–Sugeno (T–S) system and a given set of desired trajectories. The design of an output feedback controller includes a weighted contribution of the models included in the T–S design. The proposed T–S fuzzy estimates the state variables based on the output information, exclusively. The output-based controller design uses a time-dependent Lyapunov function yielding the characterisation of ultimate boundedness for the trajectory tracking error. Sufficient conditions are obtained to ensure the existence of positive-definite solutions for two coupled time-varying matrix Riccati equations, which are needed to solve the tracking problem. A simplified scheme determines the gains for the feedback controller and observer. The proposed control law solves the trajectory tracking of an autonomous underwater vehicle. In this case, numerical solutions show that the controller forced the convergence of the tracking error after 2.0 seconds. An alternative control design approach based on linear matrix inequalities (LMI) is used for comparison purposes. The suggested controller forces a faster convergence of the tracking error than the LMI-based one and provides a smaller ultimate bound.

中文翻译：

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基于时变输出的不确定非线性系统Takagi-Sugeno模糊控制器

本文证明了由 Takagi-Sugeno (T-S) 系统表示的不确定非线性系统的状态与给定的一组期望轨迹之间的轨迹跟踪问题的最终有界分析。输出反馈控制器的设计包括 T-S 设计中模型的加权贡献。所提出的 T-S 模糊估计基于输出信息的状态变量，专门。基于输出的控制器设计使用依赖于时间的李雅普诺夫函数，产生轨迹跟踪误差的极限有界的表征。获得了足够的条件来保证求解跟踪问题所需的两个耦合时变矩阵Riccati方程的正定解存在。一个简化的方案决定了反馈控制器和观测器的增益。所提出的控制律解决了自主水下航行器的轨迹跟踪问题。在这种情况下，数值解表明控制器在 2.0 秒后强迫跟踪误差收敛。基于线性矩阵不等式 (LMI) 的替代控制设计方法用于比较目的。与基于 LMI 的控制器相比，建议的控制器强制跟踪误差更快收敛，并提供更小的最终界限。基于线性矩阵不等式 (LMI) 的替代控制设计方法用于比较目的。与基于 LMI 的控制器相比，建议的控制器强制跟踪误差更快收敛，并提供更小的最终界限。基于线性矩阵不等式 (LMI) 的替代控制设计方法用于比较目的。与基于 LMI 的控制器相比，建议的控制器强制跟踪误差更快收敛，并提供更小的最终界限。