Geodesic
Learning neural network controllers for stabilizing hybrid dynamic systems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 3, pp. 354-360.

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

Control modules based on artificial neural networks (NN) are often used for controlling objects with lumped parameters. Controled objects in such systems have finite set of natural oscillation frequencies. Thereby applying NN-based controllers after setting appropriate internal parameters (learning) minimize or fully exclude probability of appearing unstable natural oscillation frequencies for a long period of time. On the other hand if the controlled object includes objects with distributed parameters (such as elastic rods) the number of its natural oscillation frequencies is at least countable infinite. Thus, for using NN-based controlers for such systems additional check of stability is needed. In case of using classic controllers (such as PID-controller) stability is guarantied by choosing internal parameters of controller from the area of stability of the system. Such approach is not applyable for NN-based controllers since their parameters are determed during the learning process. This article develops the rule which guaranties that after the learning process set of NN weights will belong to the area of stability of the system. That rule in fact appears as modification of loss function and does not apply valuable limitations on choosing a learning method. The obtained results could be used in cases of controlling hybrid dynamic systems with help of control modules based on feedforward neural networks. 
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D. K. Andreichenko; F. M. Zhadaev. Learning neural network controllers for stabilizing hybrid dynamic systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 3, pp. 354-360. http://geodesic.mathdoc.fr/item/ISU_2018_18_3_a10/

[1] Luoren L., Jinling L., “Research of PID Control Algorithm Based on Neural Network”, Energy Procedia, 13 (2011), 6988–6993 | DOI

[2] MacKunis W., Leve F., Patre P. M., Fitz-Coy N., Dixon W. E., “Adaptive neural network-based satellite attitude control in the presence of CMG uncertainty”, Aerospace Science and Technology, 2016, no. 54, 218–228 | DOI

[3] Ajorkar A., Fazlyab A., Saberi F. F., Kabganian M., “Design of an Adaptive-Neural Network Attitude Controller of a Satellite using Reaction Wheels”, JACM. 2014, 1:2, 67–73 | DOI

[4] MacKunis W., Dupree K., Bhasin S., Dixon W. E., “Adaptive neural network satellite attitude control in the presence of inertia and CMG actuator uncertainties”, 2008 American Control Conference, 2008, 2975–2980 | DOI

[5] Sivaprakash N., Shanmugam J., “Neural network based three axis satellite attitude control using only magnetic torquers”, 24th Digital Avionics Systems Conference, v. 2, 2005, 6 | DOI

[6] Andreichenko D. K., Andreichenko K. P., “On the theory of hybrid dynamical systems”, J. Comput. Syst. Sci. Int., 39:3 (2000), 383–398 | MR

[7] Andreichenko D. K., Andreichenko K. P., Modeling, analysis and synthesis of hybrid dynamic systems, Schoolbook, Publ. House “Write-Expo”, Saratov, 2013, 144 pp.

[8] Portenko M. S., Melnichuk D. V., Andreichenko D. K., “Analyticity conditions of characteristic and disturbing quasipolynomials of hybrid dynamical systems”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 16:2 (2016), 208–217 (in Russian) | DOI | MR | Zbl

[9] Andreichenko K. P., Nikishov D. A., Zhadaev F. M., “The Synthesis of Transfer Function of Neural Network in NN Control Module”, Reports of Military Sciences Academy, 2016, no. 2(70), 13–15 | MR

[10] Andreichenko D. K., Andreichenko K. P., Komarova M. S., “The Choice of Optimal Parameters for Combined Dynamical Systems”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 13:1–2 (2013), 7–11 | Zbl

[11] Andreichenko D. K., Andreichenko K. P., Komarova M. S., “Parameter Selection and Dynamic Analysis of Gas Jet Stabilization Systems with Elastic Rods”, J. Comput. Syst. Sci. Int., 51:4 (2012), 573–586 | DOI | MR | Zbl

[12] Andreichenko D. K., Andreichenko K. P., Kononov V. V., “Parallel Algorithm of Optimal Parameters Calculation for the Single Channel Angular Stabilization System”, Izv. Saratov Univ. (N. S.), Ser. Math. Mesh. Inform., 13:4-1 (2013), 109–117 (in Russian)

[13] Andreichenko D. K., Andreichenko K. P., Melnichuk D. V., Portenko M. S., “Adaptive Algorithm of Parametric Synthesis of Hybrid Dynamical Systems”, Izv. Saratov Univ. (N. S.), Ser. Math. Mesh. Inform., 16:4 (2016), 465–475 (in Russian) | DOI | MR

[14] Andreichenko D. K., Andreichenko K. P., Kononov V. V., “A Parallel Algorithm for the Parametric Synthesis of a System for the Angular Stabilization of a Rotating Elastic Beam under the Action of Longitudinal Acceleration”, J. Comput. Syst. Sci. Int., 56:2 (2017), 192–207 | DOI | DOI | MR | Zbl

[15] Robitaille B., Marcos B., Veillette M., Payre G., “Quasi-Newton methods for training neural networks”, WIT Transactions on Information and Communications Technologies, 2, 1993, 323–335 | DOI