A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA

Ervedoza S, Zuazua E (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Discrete and Continuous Dynamical Systems-Series B American Institute of Mathematical Sciences (AIMS)

Book Volume: 14

Pages Range: 1375-1401

Journal Issue: 4

DOI: 10.3934/dcdsb.2010.14.1375

Abstract

We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z(0) in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability assumptions on the adjoint system, when A generates a C(0) group, we develop a method to compute algorithmically a control function v that inherits the regularity of the initial datum to be controlled. In particular, the controlled equation is satisfied in a strong sense when the initial datum is smooth. In this way, the controlled trajectory is smooth as well. Our method applies mainly to time-reversible infinite-dimensional systems and, in particular, to the wave equation, but fails to be valid in the parabolic frame.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Université Fédérale de Toulouse Midi-Pyrénées

France (FR) Ikerbasque (Basque Foundation for Science)

Spain (ES)

How to cite

APA:

Ervedoza, S., & Zuazua, E. (2010). A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA. Discrete and Continuous Dynamical Systems-Series B, 14(4), 1375-1401. https://doi.org/10.3934/dcdsb.2010.14.1375

MLA:

Ervedoza, Sylvain, and Enrique Zuazua. "A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA." Discrete and Continuous Dynamical Systems-Series B 14.4 (2010): 1375-1401.

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