Geodesic
Optimal two-sided boundary control of heat transmission in a~rod. Hyperbolic model
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 54-60

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We consider mixed problem for one-dimensional hyperbolic system of thermal conductivity equations. We construct a class of boundary controls that provide given distribution on phase vector $(T,q)$ in a given moment of time. From this class we choose a control by the Lagrange method that minimize a square functional of loss.
Keywords: hyperbolic conductivity, boundary phase vector control, reduction of boundary control to starting one, Riemann matrices of first and second kind. 
@article{IVM_2016_6_a5,
     author = {R. K. Romanovskii and Yu. A. Medvedev},
     title = {Optimal two-sided boundary control of heat transmission in a~rod. {Hyperbolic} model},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--60},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_6_a5/}
}
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R. K. Romanovskii; Yu. A. Medvedev. Optimal two-sided boundary control of heat transmission in a~rod. Hyperbolic model. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 54-60. http://geodesic.mathdoc.fr/item/IVM_2016_6_a5/