Geodesic
On tracking solutions of parabolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 40-48

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We consider a control problem for a parabolic equation. It consists in constructing an algorithm for finding a feedback control such that a solution of a given equation should track a solution of another equation generated by an unknown right-hand side. We propose two noise-resistant solution algorithms for the indicated problem. They are based on the extremal shift method well-known in the guaranteed control theory. The first algorithm is applicable in the case of “continuous” measuring of phase states, whereas the second one implies discrete measuring.
Keywords: systems with distributed parameters, control. 
@article{IVM_2012_1_a4,
     author = {V. I. Maksimov},
     title = {On tracking solutions of parabolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {40--48},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/}
}
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V. I. Maksimov. On tracking solutions of parabolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 40-48. http://geodesic.mathdoc.fr/item/IVM_2012_1_a4/