支持向量机α阶逆系统控制—离散非线性系统

Support vector machines α th-order inverse control—nonlinear discrete systems

针对传统逆系统方法中逆模型难以建立的问题,提出了基于最小二乘支持向量机(LS-SVM)的α阶时延逆系统控制方法.通过分析LS-SVM的函数拟合特性,以离散非线性系统为例,证明了基于LS-SVM阶时延逆系统存在的充分条件.利用具有径向基(RBF)核函数的LS-SVM,离线建立了被控对象的非线性逆模型.把得到的逆系统串连在原系统之前,得到基本上线性化的伪线性复合系统,将复杂的非线性问题转化为线性问题,利用线性系统的理论实现了伪线性系统的综合.仿真结果表明,该方法适应于较一般的离散非线性系统,且在没有被控对象先验知识的情况下,能准确地建立非线性系统的逆模型.

To deal with the difficulties of inverse modelling in the traditional inverse system method, an α th-order time-delay inverse system control method based on least squares support vector machines （LS-SVM） was proposed. After the fitting characteristic of LS-SVM function was analyzed, the nonlinear discrete system was taken as an example, and a sufficiency condition for the existence of an α th -order timedelay inverse system based on LS-SVM was proved. The nonlinear inverse model of the controlled object was offline built by LS-SVM with the radial basis function （RBF） kernel function. When cascading with LS-SVM α th-order inverse system before the original system, a pseudo-linear compound system with basal linearization was formed. A complex nonlinear problem was changed into a linear problem, and the pseudolinear system was synthesized using linear system theory. Simulation results show that the method can apply to general nonlinear discrete systems and accurately model the inverse system of the nonlinear system without prior knowledge about the controlled object.