Geodesic
Optimal boundary control by displacement at one end of a string under a given elastic force at the other end
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 151-158
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The problem of optimal boundary control by displacement at one end of a string in the presence of a specified force mode at the other end is studied in the sense of a generalized solution of the corresponding mixed initial- boundary value problem from a Sobolev space. The problem of choosing an optimal boundary control from the infinite number of admissible controls is solved. A generalized solution of the mixed initial-boundary value problem is constructed explicitly and the uniqueness of the solution is proved.
Keywords: optimal control, boundary control, hyperbolic equations, wave equation. 
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E. I. Moiseev; A. A. Kholomeeva. Optimal boundary control by displacement at one end of a string under a given elastic force at the other end. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 151-158. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a13/

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