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From Morse triangular form of ODE control systems to feedback canonical form of DAE control systems
Journal of the Franklin Institute ( IF 3.7 ) Pub Date : 2021-09-03 , DOI: 10.1016/j.jfranklin.2021.08.025
Yahao Chen 1 , Witold Respondek 2
Affiliation  

In this paper, we relate the feedback canonical form FBCF [24] of differential-algebraic control systems (DACSs) with the famous Morse canonical form MCF [28],[27] of ordinary differential equation control systems (ODECSs). First, a procedure called an explicitation (with driving variables) is proposed to connect the two above categories of control systems by attaching to a DACS a class of ODECSs with two kinds of inputs (the original control input u and a vector of driving variables v). Then, we show that any ODECS with two kinds of inputs can be transformed into its extended MCF via two intermediate forms: the extended Morse triangular form and the extended Morse normal form. Next, we illustrate that the FBCF of a DACS and the extended MCF of the explicitation system have a perfect one-to-one correspondence. At last, an algorithm is proposed to transform a given DACS into its FBCF via the explicitation procedure and a numerical example is given to show the efficiency of the proposed algorithm.



中文翻译:

从 ODE 控制系统的莫尔斯三角形式到 DAE 控制系统的反馈规范形式

在本文中,我们将微分代数控制系统 (DACS)的反馈规范形式FBCF [24] 与常微分方程控制系统 (ODECS)的著名莫尔斯规范形式MCF [28]、[27] 联系起来。首先,提出了一种称为显化(带有驱动变量)的程序,通过将一类具有两种输入(原始控制输入 和驱动变量的向量 v)。然后,我们证明了任何具有两种输入的 ODECS 都可以通过两种中间形式转换为其扩展的MCF:扩展的莫尔斯三角形式和扩展的莫尔斯范式。接下来,我们说明了FBCF一个DACS和扩展MCF的明晰化系统拥有完美的一对一一对应。最后,提出了一种通过显式过程将给定的DACS转换为其FBCF的算法,并给出了一个数值例子来说明所提出算法的效率。

更新日期:2021-10-13
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