基于数据的一类部分未知仿射非线性系统近似解

Data-based Approximate Solution for a Class of Affine Nonlinear Systems with Partially Unknown Functions

针对一类部分未知仿射非线性系统无穷区间求解问题,利用在线采样数据,提出了在线无偏最小二乘支持向量机(Least square support vector machines,LS-SVM)的方法.首先,通过引入一个参数消除了LS-SVM的偏置项,避免了冗余计算,同时在优化目标中引入权值函数,对靠近当前时刻的数据样本点赋予更高权重,提高了计算精度;其次,采用滚动时间窗的方法,实现非线性系统无穷区间求解,并满足求解实时性要求;最后,通过数值算例仿真验证了本文方法的有效性和优越性.

A new method named online unbiased least square support vector machines （LS-SVMs） is proposed by using online sampling data to find the approximate solution of a class of partially unknown affine nonlinear systems within the infinite interval. Firstly, we eliminate the bias of LS-SVMs by introducing a parameter to avoid redundant computation, meanwhile, we give the data points which are closer to the current moment more weights by introducing a weight function to the optimized target, thus the computational accuracy is improved. Secondly, the method of sliding time window is employed to achieve the approximate solution for affine nonlinear systems within the infinite interval and meet the requirement of real-time solving. Finally, simulations of numerical examples demonstrate the efficiency and superiority of the proposed method.