基于反馈和多最小二乘支持向量机的分数阶混沌系统控制  

Fractional order chaotic system control based on feedback and multiple least square support vector machines

作　　者：杨红[1] 王瑞[2] 

机构地区：[1]广州大学,物理与电子工程学院,广州510006 [2]华南理工大学,自动化科学与工程学院,广州510641

出　　处：《物理学报》2011年第7期105-111,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60774032);教育部高等学校博士学科点专项科研基金(批准号:20070561006)资助的课题~~

摘　　要：根据分数阶线性系统的稳定理论,将混沌系统分成稳定的线性部分和相应的非线性部分.设计主动控制器,对非线性部分进行补偿,从而将分数阶混沌系统控制到平衡点.为了提高主动控制器的补偿能力,提出基于反馈的多最小二乘支持向量机(M-LS-SVM)拟合模型.通过减聚类方法将输入空间划分为一些小的局部空间,在每个局部空间中用LS-SVM建立子模型.为解决子模型相互之间的严重相关问题,提高模型的精度和鲁棒性,各个子模型的预测输出通过主元递归(PCR)方法连接.仿真实验表明该方法有助于提高补偿精度和系统响应指标.According to the stability of fractional order linear systems theory, the system is decomposed into stable linear parts and the corresponding nonlinear parts. The active controller is designed to compensate the nonlinear parts, and the fractional order chaotic system is suppressed to an equilibrium point. In order to improve the compensation ability of active controller, a multiple least square support vector machine （M-LS-SVM） regression model is presented based on feedback. The subtractive clustering is adopted to divide the input space into several sub-spaces, and sub-models are built by a LS- SVM in each sub-space. In order to minimize the severe correlation among sub-models and to improve the accuracy and the robustness of the model, the sub-models are combined by principal component regression （PCR）. The experiment result shows that by using the method the compensation accuracy and the system response indices can be improved.

关 键 词：分数阶 混沌系统 多最小二乘支持向量机 反馈 

分 类 号：O415.5[理学—理论物理]