基于矩阵半张量积方法的随机模糊系统控制器设计

Controller design of stochastic fuzzy systems based on the semi-tensor product method of matrices

利用矩阵半张量积理论研究了随机模糊逻辑和随机模糊系统的控制器设计问题。给出了随机模糊逻辑的概念及相关性质;基于半张量积理论研究了随机模糊控制器,并给出了随机模糊规则的表示形式;确定了随机模糊控制器的结构矩阵和概率转移矩阵,得到了随机模糊推理的代数表达式。数值例子说明了该方法的有效性。

The stochastic fuzzy logic and controller design of stochastic fuzzy systems were investigated based on the the-ory of semi-tensor product of matrices, and some new results about stochastic fuzzy logic and stochastic fuzzy systems were obtained. First, some concepts and properties on stochastic fuzzy logic were given. Then, the design of stochastic fuzzy controller was studied based on the semi-tensor product method, and the new expression of stochastic fuzzy rules was presented. Based on the new expression of fuzzy rules, the complex stochastic fuzzy reasoning was converted into the simple algebraic equation by constructing the structure matrix and the transition probability matrix. Finally, a numer-ical example was provided to demonstrate our new results.