Realization of discrete-time nonlinear input-output equations: polynomial approach
Realization of discrete-time nonlinear input-output equations: polynomial approach
复制标题
离散时间非线性输入输出方程的实现：多项式方法
DOI：
10.1016/j.automatica.2011.07.010
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Tõnso
中科院分区：
文献类型：
--
作者：
Ü. Kotta;M. Tõnso
本文的目的是应用非交换多项式理论解决离散多输入多输出非线性控制系统的约简与实现问题。首先，利用系统高阶输入输出差分方程的最大公约数，给出了系统高阶输入输出差分方程的两个多项式矩阵的最大公约数的充要条件。该条件还提供了一种系统约简的方法，即寻找i/o方程组的不可约表示，使其与原系统表示传递等价。其次，为了解决实现问题，提出了直接从非线性系统的多项式描述中计算状态坐标微分的公式。本文讨论的多项式方法更直接，并且比以前用微分一形式的子空间表示的方法需要明显更少的计算。
The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common left divisor of two polynomial matrices associated with the set of the higher order input–output (i/o) difference equations of the system. The condition also provides a method for system reduction, i.e. for finding the irreducible representation of the set of the i/o equations, being transfer equivalent to the original system representation. Second, to solve the realization problem, a formula is presented for computing the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The polynomial approach addressed in this paper is more direct and requires noticeably less computations than earlier methods represented in terms of subspaces of differential one-forms.