The discretized backstepping method: An application to a general system of $ 2\times 2 $ linear balance laws | Zendy

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The discretized backstepping method: An application to a general system of $ 2\times 2 $ linear balance laws

Author(s) -

Mathias Dus

Publication year - 2022

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2022006

Subject(s) - backstepping , discretization , balance (ability) , scheme (mathematics) , mathematics , control theory (sociology) , construct (python library) , computer science , control (management) , law , mathematical analysis , adaptive control , artificial intelligence , medicine , political science , physical medicine and rehabilitation , programming language

In this paper, we introduce the numerical backstepping method by applying it to a problem of finite-time stabilization for a system of \begin{document}$ 2 \times 2 $\end{document} balance laws discretized thanks to the upwind scheme. On the one hand, we illustrate on an example that the scheme used to compute the feedback control cannot be chosen arbitrarily. On the other hand, an algorithm is given to construct this control properly and an approached finite-time stabilization result is proven.

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