On geometric and differentiation index of nonlinear differential-algebraic equations

被引:6
作者
Chen, Yahao [1 ]
Trenn, Stephan [1 ]
机构
[1] Univ Groningen, Bernoulli Inst Math Comp Sci & Artificial Intelli, Groningen, Netherlands
关键词
differential-algebraic equations; geometric method; differentiation index; geometric index; existence and uniqueness of solutions; FORM;
D O I
10.1016/j.ifacol.2021.06.075
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We discuss two notions of index, i.e., the geometric index and the differentiation index for nonlinear differential-algebraic equations (DAEs). First, we analyze solutions of nonlinear DAEs by revising a geometric reduction method (see e.g. Rabier and Rheinboldt (2002),Riaza (2008)). Then we show that although both of the geometric index and the differentiation index serve as a measure of difficulties for solving DAEs, they are actually related to the existence and uniqueness of solutions in a different manner. It is claimed in (Campbell and Gear, 1995) that the two indices coincide when sufficient smoothness and assumptions are satisfied, we elaborate this claim and show that the two indices indeed coincide if and only if a condition of uniqueness of solutions is satisfied (under certain constant rank assumptions). Finally, an example of a pendulum system is used to illustrate our results on the two indices. Copyright (C) 2021 The Authors.
引用
收藏
页码:186 / 191
页数:6
相关论文
共 22 条
[2]   Controlled invariance for nonlinear differential-algebraic systems [J].
Berger, Thomas .
AUTOMATICA, 2016, 64 :226-233
[3]   THE QUASI-KRONECKER FORM FOR MATRIX PENCILS [J].
Berger, Thomas ;
Trenn, Stephan .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2012, 33 (02) :336-368
[4]  
Brenan K.E., 1996, NEMERICAL SOLUTION I, V14
[5]   HIGH-INDEX DIFFERENTIAL-ALGEBRAIC EQUATIONS [J].
CAMPBELL, SL .
MECHANICS OF STRUCTURES AND MACHINES, 1995, 23 (02) :199-222
[6]   THE INDEX OF GENERAL NONLINEAR DAES [J].
CAMPBELL, SL ;
GEAR, CW .
NUMERISCHE MATHEMATIK, 1995, 72 (02) :173-196
[7]   SOLVABILITY OF GENERAL DIFFERENTIAL-ALGEBRAIC EQUATIONS [J].
CAMPBELL, SL ;
GRIEPENTROG, E .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1995, 16 (02) :257-270
[8]  
Chen Y., 2021, GEOMETRIC ANAL UNPUB
[9]   GEOMETRIC ANALYSIS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS VIA LINEAR CONTROL THEORY [J].
Chen, Yahao ;
Respondek, Witold .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2021, 59 (01) :103-130
[10]   DIFFERENTIAL-ALGEBRAIC EQUATION INDEX TRANSFORMATIONS [J].
GEAR, CW .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1988, 9 (01) :39-47