Diagnostic algorithms in some systems of direct and indirect control

M. V. Shamolin

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 205 (2022), pp. 107-118.

Résumé

We discuss the diagnostics of malfunctions in a system of indirect control of an object whose motion is governed by third-order nonlinear ordinary differential equations (B. V. Bulgakov's problem). We also consider diagnostics of malfunctions in one system of direct control of the aircraft described by second-order nonlinear differential equations. Using methods developed earlier, we construct a diagnostic algorithm.

Détail

Keywords: problem of differential diagnostics, indirect control system, direct control system, diagnostics, sphere of control, asymptotic stability.

Bibliographie

[1] Borisenok I. T., Shamolin M. V., “Reshenie zadachi differentsialnoi diagnostiki”, Fundam. prikl. mat., 5:3 (1999), 775–790 | MR | Zbl

[2] Borisenok I. T., Shamolin M. V., “Reshenie zadachi differentsialnoi diagnostiki metodom statisticheskikh ispytanii”, Vestn. Mosk. un-ta. Ser. 1. Mat. Mekh., 2001, no. 1, 29–31 | MR | Zbl

[3] Zhukov V. P., “O dostatochnykh i neobkhodimykh usloviyakh asimptoticheskoi ustoichivosti nelineinykh dinamicheskikh sistem”, Avtomat. telemekh., 1994, no. 3, 24–36 | Zbl

[4] Mironovskii L. A., “Funktsionalnoe diagnostirovanie dinamicheskikh sistem”, Avtomat. telemekh., 1980, no. 3, 96–121.

[5] Okunev Yu. M., Sadovnichii V. A., Samsonov V. A., Chernyi G. G., “Kompleks modelirovaniya zadach dinamiki poleta”, Vestn. Mosk. un-ta. Ser. 1. Mat. Mekh., 1996, no. 6, 66–75 | Zbl

[6] Parkhomenko P. P., Sagomonyan E. S., Osnovy tekhnicheskoi diagnostiki, Energiya, M., 1981

[7] Chikin M. G., “Sistemy s fazovymi ogranicheniyami”, Avtomat. telemekh., 1987, no. 10, 38–46 | MR | Zbl

[8] Shamolin M. V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela, «Ekzamen», M., 2004

[9] Shamolin M. V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela. Izd. 2, «Ekzamen», M., 2007

[10] Shamolin M. V., “Diagnostika neispravnostei v odnoi sisteme nepryamogo upravleniya”, Elektron. model., 31:4 (2009), 55–66

[11] Shamolin M. V., “Rasshirennaya zadacha differentsialnoi diagnostiki i ee vozmozhnoe reshenie”, Elektron. model., 31:1 (2009), 97–115

[12] Shamolin M. V., “Reshenie zadachi diagnostirovaniya v sluchae tochnykh traektornykh izmerenii s oshibkoi”, Elektron. model., 31:3 (2009), 73–90

[13] Shamolin M. V., “Diagnostika dvizheniya letatelnogo apparata v rezhime planiruyuschego spuska”, Elektron. model., 32:5 (2010), 31–44

[14] Shamolin M. V., “Diagnostika odnoi sistemy pryamogo upravleniya dvizheniem letatelnykh apparatov”, Elektron. model., 32:1 (2010), 45–52

[15] Shamolin M. V., “Diagnostika girostabilizirovannoi platformy, vklyuchennoi v sistemu upravleniya dvizheniem letatelnogo apparata”, Elektron. model., 33:3 (2011), 121–126

[16] Shamolin M. V., “Reshenie zadachi diagnostirovaniya v sluchayakh traektornykh izmerenii s oshibkoi i tochnykh traektornykh izmerenii”, Itogi nauki tekhn. Ser. Sovr. mat. prilozh. Temat. obz., 150 (2018), 88–109 | MR

[17] Shamolin M. V., “Zadachi differentsialnoi i topologicheskoi diagnostiki. Ch. 1. Uravneniya dvizheniya i klassifikatsiya neispravnostei”, Vestn. Samar. un-ta. Estestvennonauch. ser., 25:1 (2019), 32–43 | MR | Zbl

[18] Shamolin M. V., “Zadachi differentsialnoi i topologicheskoi diagnostiki. Ch. 2. Zadacha differentsialnoi diagnostiki”, Vestn. Samar. un-ta. Estestvennonauch. ser., 25:3 (2019), 22–31 | MR

[19] Shamolin M. V., “Zadachi differentsialnoi i topologicheskoi diagnostiki. Ch. 3. Zadacha kontrolya”, Vestn. Samar. un-ta. Estestvennonauch. ser., 25:4 (2019), 36–47 | MR | Zbl

[20] Shamolin M. V., “Zadachi differentsialnoi i topologicheskoi diagnostiki. Ch. 4. Zadacha diagnostirovaniya (sluchai tochnykh traektornykh izmerenii)”, Vestn. Samar. un-ta. Estestvennonauch. ser., 26:1 (2020), 36–47 | MR

[21] Shamolin M. V., Krugova E. P., “Zadacha diagnostiki modeli girostabilizirovannoi platformy”, Itogi nauki tekhn. Ser. Sovr. mat. prilozh. Temat. obz., 160 (2019), 137–141 | MR

[22] Aleksandrov A. Y., Aleksandrova E. B., Tikhonov A. A., “On the monoaxial stabilization of a rigid body under vanishing restoring torque”, AIP Conf. Proc., 1959 (2018), 080001 | DOI | MR

[23] Altman E., Avrachenkov K., Menache I., Miller G., Prabhu B. J., Shwartz A., “Power control in wireless cellular networks”, IEEE Trans. Automat. Control., 54:10 (2009), 2328–2340 | DOI | MR | Zbl

[24] Antoulas A. C., Sorensen D. C., Zhou Y., “On the decay rate of Hankel singular values and related issues”, Syst,. Control Lett., 46 (2002), 323–342 | DOI | MR | Zbl

[25] Beck A., Teboulle M., “Mirror descent and nonlinear projected subgradient methods for convex optimization”, Oper. Res. Lett., 31:3 (2003), 167–175 | DOI | MR | Zbl

[26] Ben-Tal A., Margalit T., Nemirovski A., “The ordered subsets mirror descent optimization method with applications to tomography”, SIAM J. Optim., 12:1 (2001), 79–108 | DOI | MR | Zbl

[27] Ober R. J., “Balanced parameterization of classes of linear systems *”, SIAM J. Control Optim., 29:6 (1991), 1251–1287 | DOI | MR | Zbl

[28] Ober R. J., McFarlane D., “Balanced canonical forms for minimal systems: A normalized coprime factor approach”, Linear Algebra Appl., 122-124 (1989), 23–64 | DOI | MR | Zbl

[29] Shamolin M. V., “Foundations of differential and topological diagnostics”, J. Math. Sci., 114:1 (2003), 976–1024 | DOI | MR | Zbl

[30] Su W., Boyd S., Candes E., “A differential equation for modeling Nesterov's accelerated gradient method: Theory and insights”, J. Machine Learning Res., 2016, no. 17 (153), 1–43 | MR | Zbl

[31] Tikhonov A. A., Yakovlev A. B., “On dependence of equilibrium characteristics of the space tethered system on environmental parameters”, Int. J. Plasma Env. Sci. Techn., 13:1, 49–52 | MR