分段广义正交多项式算子法的非线性系统分析

Analysis of Nonlinear Time-Varying Systems via Piecewise General Orthogonal Polynomials Operator

首先对文献 [7]提出的分段广义正交多项式算子 (简记为PGOPO)的主要运算规则进行了概括和总结 ,特别是推导出了非线性函数的PGOPO递推计算公式 ;其次对一般非线性系统PGOPO算子解及解的收敛性问题进行了分析、研究 ,证明了PGOPO算子解将收敛于其精确解 ;最后采用PGOPO算子法对一类含时延的非线性系统进行了分析 ,并推导出便于使用的递推求解算法。给出的数值算例论证了该算法的有效性。

Based on general hybrid orthogonal functions, the main operational rules of a new linear, continuous and bounded operator PGOPO are established systematically, and the approximation formulations of nonlinear function are given especially. The convergence in the mean square of the piecewise general orthogonal polynomials solutions to the nonlinear systems is proved. Algorithms for the analysis of nonlinear delay system are given. Computational example is presented to illustrate the utility of the method.