摘要
定义了一类新的正交函数系——按段多重Chebyshev多项式系,研究了该函数系的一些基本性质和运算法则,得出了积分运算等运算矩阵,并将此多项式系应用于线性系统分析和参数估计,获得了简单、快速的递推算法。仿真结果表明,采用本算法进行系统状态估计和参数辨识,结果显著优于移位Chebyshev多项式系所导出的算法。
A new kind of orthogonal polynomials——Piecewise Multiple Chebyshev Polynomials is defined and its main properties are discussed. The integral operational matrix is also proposed. Based on this technique, studies on system analysis and parameter estimation of linear systems arc conducted, and two simple, quickly-calculated and iterative algorithms are obtained. The results of two examples show that the algorithms proposed arc better than that in references.
基金
国家自然科学基金(编号:6884021)
关键词
正交多项式
CHEBYSHEV
正交函数
orthogonal function
orthogonal polynomials
approximation by polynom-ials
time-invariant systems
parameter estimation
systems analysis
linear systems
