分数布朗运动驱动的广义模糊系统的滑模控制

Sliding mode control for singular fuzzy systems driven by fractional Brownian motions

研究了分数布朗运动驱动下时滞广义T-S模糊系统的滑模控制。首先将T-S模糊系统模糊混合后得到了模糊模型,针对此模型构造了滑模面函数和设计滑模控制器。目前处理分数布朗运动的Lyapunov泛函多采用指数型,该类型Lyapunov泛函有一定的保守性,因此构造了一类新型Lyapunov泛函,然后通过线性矩阵不等式以及Gronwall不等式分析了滑动模态的有限时间随机有界问题,给出了有限时间随机有界的充分条件。为了保证模糊系统能在有限时间内到达滑模面讨论了滑模的有限时间可达性。最后通过数值算例验证了以上结论的有效性。

This study deals with the sliding mode control for singular T-S fuzzy systems with time delays driven by fractional Brownian motions.Firstly,after mixing T-S fuzzy system by fuzzy model,a sliding mode surface function and a sliding mode controller are designed according to the model structure.Presently the exponential-type Lyapunov functional is usually utilized to deal with the fractional Brownian motions,and this type Lyapunov functional is conservative to some extent.Thus,a new-type Lyapunov functional is constructed.The finite-time stochastic boundedness problem for the sliding mode dynamics is analyzed by linear matrix inequality and Gronwall inequality,and some sufficient conditions are given.To ensure that the fuzzy system can reach to the sliding surface in a finite time,the reachability of the sliding mode surface is investigated.Finally,a numerical example is given to verify the effectiveness of the proposed results.