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A minimal energy control problem for second‐order linear hyperbolic systems with two independent variables
Author(s) -
Hasanov K. K.,
Gasumov T. M.
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.978
Subject(s) - controllability , mathematics , degeneracy (biology) , matrix (chemical analysis) , order (exchange) , representation (politics) , pure mathematics , optimal control , riemann surface , energy (signal processing) , mathematical analysis , mathematical optimization , law , bioinformatics , materials science , finance , politics , political science , economics , composite material , biology , statistics
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 →ℝ m and z : D →ℝ n . 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 ( x 1 , y 1 ) = 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.