A minimal energy control problem for second-order linear hyperbolic systems with two independent variables

SUMMARY In this paper, we investigate controllability and minimal energy optimal control for Goursat–Darboux problem for the second‐order linear hyperbolic systems with two independent variables. The equation describes a relation between functions u: D→ℝm and z: D→ℝn. We get an integral representati...

Full description

Saved in:
Bibliographic Details
Published inOptimal control applications & methods Vol. 33; no. 1; pp. 51 - 60
Main Authors Hasanov, K. K., Gasumov, T. M.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.01.2012
Subjects
controllability
l-moments problem
nondegenerate
optimal control
Riemann matrix
Online AccessGet full text

Cover

More Information
Summary:SUMMARY In this paper, we investigate controllability and minimal energy optimal control for Goursat–Darboux problem for the second‐order linear hyperbolic systems with two independent variables. The equation describes a relation between functions u: D→ℝm and z: D→ℝn. We get an integral representation of the Goursat–Darboux problem by means of Riemann's matrix. The first half of the paper considers conditions under which there exists a control u for which the solution z of dynamics satisfies z(x1, y1) = p for any given p. The studied problem is reduced to the moments problem. The optimal control was found in a closed analytic form. Further, degeneracy of the matrix constructed by means of Riemann's matrix is shown to be a necessary and sufficient condition of controllability. Copyright © 2011 John Wiley & Sons, Ltd.
Bibliography:ArticleID:OCA978
ark:/67375/WNG-MPMBJ241-L
istex:A160F07F4EF7810DA220AE09CF784E44CB17789C
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.978