INTERNAL RAPID STABILIZATION OF A 1-D LINEAR TRANSPORT EQUATION WITH A SCALAR FEEDBACK

Zhang C (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Mathematical Control and Related Fields American Institute of Mathematical Sciences (AIMS)

Book Volume: 12

Pages Range: 169-200

Journal Issue: 1

DOI: 10.3934/mcrf.2021006

Abstract

We use a variant the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate. The variant of the backstepping method used here relies mainly on the spectral properties of the linear transport equation, and leads to some original technical developments that differ substantially from previous applications.

Authors with CRIS profile

Christophe Zhang Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Zhang, C. (2022). INTERNAL RAPID STABILIZATION OF A 1-D LINEAR TRANSPORT EQUATION WITH A SCALAR FEEDBACK. Mathematical Control and Related Fields, 12(1), 169-200. https://dx.doi.org/10.3934/mcrf.2021006

MLA:

Zhang, Christophe. "INTERNAL RAPID STABILIZATION OF A 1-D LINEAR TRANSPORT EQUATION WITH A SCALAR FEEDBACK." Mathematical Control and Related Fields 12.1 (2022): 169-200.

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