T-S模糊系统的自触发有限时间H∞控制

Self-triggering Finite Time H∞ Control for T-S Fuzzy Systems

摘要:

为克服事件触发控制对硬件设备的依赖以及控制策略频繁更新的局限，针对一类不确定Takagi-Sugeno（T-S）模糊系统的有限时间H∞控制问题，引入自触发机制，提出一种基于此机制下只与触发时刻状态有关的模糊控制器设计方法；基于自触发机制并结合有限时间控制的思想，通过设计触发间隔函数、推导并求解线性矩阵不等式（LMI），使得系统在保障稳定性的前提下，系统运动轨迹不会超过一定的界限，并达到所期望H∞性能水平；同时相较于事件触发机制，自触发机制位于系统内部，无需额外硬件设备接收触发信号且只需利用当前的触发状态信息来预测下一触发时刻，在一定程度上进一步降低系统资源成本；此外，利用李亚普诺夫函数对系统稳定性进行了严格分析，并提供一个确保能够防止芝诺现象发生的证明；最后，通过数值仿真、单连杆刚性机器人系统实例仿真两个实验说明所提方法的有效性。

Abstract:

In order to overcome the dependence of event-triggering control on hardware devices and the limitation of frequent update of control strategy, a self-triggering mechanism is introduced for the finite time H∞ control problem of a class of uncertain Takagi-Sugeno (T-S) fuzzy systems, and a fuzzy controller design method based on this mechanism is proposed. Based on the self-triggering mechanism and the idea of finite-time stability, by designing the triggering interval function, deducing and solving the linear matrix inequality (LMI), the system trajectory will not exceed a certain limit and reach the desired H∞ performance level under the premise of ensuring stability. At the same time, compared with the event trigger mechanism, the self-trigger mechanism is located in the system, without additional hardware devices to receive trigger signals, and only needs to use the current trigger state information to predict the next trigger moment, which further reduces the system resource cost to a certain extent. In addition, the stability of the system is analyzed strictly by means of Lyapunov function, and a proof to prevent Zeno phenomenon is provided. Finally, the effectiveness of the proposed method is demonstrated by numerical simulation and example simulation of a single-link rigid robot system.