A minimal energy control problem for second‐order linear hyperbolic systems with two independent variables | Zendy

Hasanov K. K. | Zendy; Gasumov T. M. | Zendy

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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.

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