Normal forms and internal regularization of nonlinear differential-algebraic control systems

Yahao Chen*, Stephan Trenn, Witold Respondek

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

In this article, we propose two normal forms for nonlinear differential-algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, that is, when there exists a state feedback transforming the DACS into a differential-algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs.
Original languageEnglish
Pages (from-to) 6562-6584
JournalInternational Journal of Robust and Nonlinear Control
Volume31
Issue number14
Early online date4-Jun-2021
DOIs
Publication statusPublished - 25-Sep-2021

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