Geodesic
On algorithm for numerical solution of optimal measurement problem using linear splines
Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 37-47.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an algorithm for numerical solution of the optimal measurement problem using linear splines. The optimal measurement problem, which is based on the model of optimal control, is posed to restore the dynamically distorted signal. We propose to use a mixed-control problem for Leontief type systems in the development of numerical algorithm for solution of the optimal measurement problem. Furthermore, the use of linear splines at one of the algorithm steps reduces the amount of machine time required to find an approximate solution with a given accuracy.
Keywords: numerical algorithm of the optimal measurement problem, mixed control problem, optimal control, Leontief type system, Showalter – Sidorov condition, linear splines. 
@article{JCEM_2016_3_1_a4,
     author = {A. A. Ebel},
     title = {On algorithm for numerical solution of optimal measurement problem using linear splines},
     journal = {Journal of computational and engineering mathematics},
     pages = {37--47},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a4/}
}
TY  - JOUR
AU  - A. A. Ebel
TI  - On algorithm for numerical solution of optimal measurement problem using linear splines
JO  - Journal of computational and engineering mathematics
PY  - 2016
SP  - 37
EP  - 47
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a4/
LA  - en
ID  - JCEM_2016_3_1_a4
ER  - 
%0 Journal Article
%A A. A. Ebel
%T On algorithm for numerical solution of optimal measurement problem using linear splines
%J Journal of computational and engineering mathematics
%D 2016
%P 37-47
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a4/
%G en
%F JCEM_2016_3_1_a4
A. A. Ebel. On algorithm for numerical solution of optimal measurement problem using linear splines. Journal of computational and engineering mathematics, Tome 3 (2016) no. 1, pp. 37-47. http://geodesic.mathdoc.fr/item/JCEM_2016_3_1_a4/

[1] A. L. Shestakov, “Dinamicheskaya tochnocht izmeritelnogo preobrazovatelya s korrektiruyuschim ustroistvom v vide datchika”, Metrologiya, 1987, no. 2, 26-34 | MR

[2] A. L. Shestakov, “Izmeritelnyi preobrazovatel dinamicheskikh parametrov s iteratsionnym printsipom vosstanovleniya signala”, Pribory i sistemy upravleniya, 1992, no. 10, 23-24

[3] A. L. Shestakov, M. N. Bizyaev, “Vosstanovlenie dinamicheski iskazhennykh signalov ispytatelno-izmeritelnykh sistem metodom skolzyaschikh rezhimov”, Izvestiya RAN. Energetika, 2004, no. 6, 119-130

[4] A. L. Shestakov, A. S. Volosnikov, “Neirosetevaya dinamicheskaya model izmeritelnoi sistemy s filtratsiei vosstanavlivaemogo signala”, Vestnik YuUrGU. Seriya: Kompyuternye tekhnologii, upravlenie, radioelektronika, 4:14(69) (2006), 16-20

[5] A. L. Shestakov, G. A. Sviridyuk, “Novyi podkhod k izmereniyu dinamicheski iskazhennykh signalov”, Vestnik YuUrGU. Seriya: Matematicheskoe modelirovanie i programmirovanie, 2010, no. 16(192), 116-120 | Zbl

[6] E. V. Soldatkina, Algoritmy adaptatsii parametrov izmeritelnoi sistemy k minimumu otsenki dinamicheskoi pogreshnosti, diss. ... kand. tekhn. nauk, YuUrGU, Chelyabinsk, 2000

[7] M. N. Bizyaev, Dinamicheskie modeli i algoritmy vosstanovleniya dinamicheski iskazhennykh signalov izmeritelnykh sistem v skolzyaschem rezhime, diss. ... kand. tekhn. nauk, YuUrGU, Chelyabinsk, 2004

[8] D. Yu. Iosifov, Dinamicheskie modeli i algoritmy vosstanovleniya signalov izmeritelnykh sistem s nablyudaemym vektorom koordinat sostoyaniya, diss. ... kand. tekhn. nauk, YuUrGU, Chelyabinsk, 2007

[9] A. L. Shestakov, G. A. Sviridyuk, “Optimalnoe izmerenie dinamicheski iskazhennykh signalov”, Vestnik YuUrGU. Seriya: Matematicheskoe modelirovanie i programmirovanie, 8:17(234) (2011), 70-75 | Zbl

[10] S. A. Zagrebina, “O zadache Shouoltera – Sidorova”, Izvestiya vysshikh uchebnykh zavedenii. Matematika, 2007, no. 3, 22-28 | MR | Zbl

[11] A. V. Keller, E. I. Nazarova, “Zadacha optimalnogo izmereniya: chislennoe reshenie, algoritm programmy”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya: Matematika, 2011, no. 3, 74-82 | Zbl

[12] Yu. V. Khudyakov, A. L. Shestakov, “Algoritm chislennogo issledovaniya modeli Shestakova – Sviridyuka izmeritelnogo ustroistva s inertsionnostyu i rezonansami”, Matematicheskie zametki SVFU, 20:2 (2013), 211-221 | Zbl

[13] Yu. V. Khudyakov, M. A. Sagadeeva, “Ob optimalnom izmerenii dlya modeli izmeritelnogo ustroistva s uchetom determinirovannogo multiplikativnogo vozdeistviya”, Sbornik XII Vserossiiskogo soveschaniya po problemam upravleniya, 2014, 2240–2245

[14] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, 179 pp. | MR | Zbl

[15] G. A. Sviridyuk, A. A. Efremov, “Optimalnoe upravlenie lineinymi uravneniyami tipa Soboleva s otnositelno p-sektorialnymi operatorami”, Differentsialnye uravneniya, 31:11 (1995), 1912-1919 | MR | Zbl

[16] G. A. Sviridyuk, A. A. Efremov, “Zadacha optimalnogo upravleniya dlya odnogo klassa lineinykh uravnenii tipa Soboleva”, Izvestiya vuzov. Matematika, 40:12 (1996), 75-83 | MR | Zbl

[17] N. A. Manakova, E. A. Bogonos, “Optimalnoe upravlenie resheniyami zadachi Shouoltera – Sidorova dlya odnogo uravneniya sobolevskogo tipa”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya: Matematika, 3:1 (2010), 42-53 | MR | Zbl

[18] A. A. Zamyshlyaeva, “Matematicheskie modeli sobolevskogo tipa vysokogo poryadka”, Vestnik YuUrGU. Seriya: Matematicheskoe modelirovanie i programmirovanie, 7:2 (2014), 5-28 | Zbl

[19] A. V. Keller, M. A. Sagadeeva, “Chislennoe reshenie zadach optimalnogo i zhestkogo upravleniya dlya odnoi nestatsionarnoi sistemy leontevskogo tipa”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 32:19 (162) (2013), 57-66

[20] N. A. Manakova, A. G. Dyl'kov, “Optimal Control of the Solutions of the Initial-Finish Problem for the Linear Hoff Model”, Mathematical Notes, 94:1-2 (2013), 220-230 | DOI | MR | Zbl

[21] M. V. Plekhanova, A. F. Islamova, “Zadacha so smeshannym upravleniem dlya odnogo klassa lineinykh uravnenii sobolevskogo tipa”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2010, no. 23, 49-58 | MR

[22] A. V. Keller, A. A. Ebel, “The Existence of a Unique Solution to a Mixed Control Problem for Sobolev Type Equations”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7:3 (2014), 121-127 | Zbl

[23] A. A. Ebel, “O svoistvakh funktsionala zadach smeshannogo upravleniya smeshannogo upravleniya dlya sistem leontevskogo tipa”, Yuzhno-Uralskaya molodezhnaya shkola po matematicheskomu modelirovaniyu, Cb. tr. II Vseross. nauch.-prakt. konf. (Chelyabinsk, 2015), YuUrGU, Chelyabinsk, 2015, 203-206

[24] A. V. Keller, A. A. Ebel, “Chislennyi metod resheniya zadach smeshannogo upravleniya dlya sistem leontevskogo tipa”, Vestnik YuUrGU. Seriya: Matematika. Mekhanika. Fizika, 7:4 (2015), 37-45 | Zbl

[25] A. V. Keller, M. A. Sagadeeva, “Zadacha optimalnogo izmereniya dlya modeli izmeritelnogo ustroistva s determinirovannym multiplikativnym vozdeistviem i inertsionnostyu”, Vestnik YuUrGU. Seriya: Matematicheskoe modelirovanie i programmirovanie, 7:1 (2014), 134-138 | Zbl