Multicriteria Optimization of Stochastic Robust Control of the Tracking System

Authors

Borys I. Kuznetsov, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), e-mail: kuznetsov.boris.i@gmail.com, ORCID: 0000-0002-1100-095X

Ihor V. Bovdui, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), e-mail: ibovduj@gmail.com, ORCID: 0000-0003-3508-9781

Olena V. Voloshko, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), e-mail: vinichenko.e.5@gmail.com, ORCID: /0000-0002-6931-998X

Tetyana B. Nikitina, Bakhmut Education Research and Professional Pedagogical Institute of V. N. Karazin Kharkiv National University (9a, Nosakov str., Bakhmut, 84511, Ukraine), e-mail: tatjana55555@gmail.com, ORCID: 0000-0002-9826-1123

Borys B. Kobylianskyi, Bakhmut Education Research and Professional Pedagogical Institute of V. N. Karazin Kharkiv National University (9a, Nosakov str., Bakhmut, 84511, Ukraine), e-mail: nnppiuipa@ukr.net, ORCID: 0000-0003-3226-5997

Abstract

A multicriteria optimization of stochastic robust control with two degrees of freedom of a tracking system with anisotropic regulators has been developed to increase accuracy and reduce sensitivity to uncertain object parameters. Such objects are located on a moving base, on which sensors for angles, angular velocities and angular accelerations are installed. Improvements in the accuracy of control with two degrees of freedom include closed-loop feedback control and open-loop feedback control through the use of reference and perturbation effects. The multicriteria optimization of the stochastic robust control tracking system with two degrees of freedom with anisotropic controllers is reduced to the iterative solution of a system of four coupled Riccati equations, the Lyapunov equation, and the determination of the anisotropy norm of the system by an expression of a special form, which is numerically solved using the homotopy method, which includes vectorization matrices and iterations according to Newton’s method. The objective vector of robust control is calculated in the form of a solution of a vector game, the vector gains of which are direct indicators of the quality that the system should achieve in different modes of its operation. The calculation of the vector gains of this game is related to the simulation of a synthesized system with anisotropic regulators for different modes of operation with different input signals and object parameter values. The solutions of this vector game are calculated on the basis of a set of Pareto-optimal solutions taking into account the binary relations of preferences on the basis of the metaheuristic algorithm of multi-swarm Archimedes optimization. Based on the results of the synthesis of stochastic robust control of a tracking system with two degrees of freedom with anisotropic controllers, it is shown that the use of synthesized controllers made it possible to increase the accuracy of system control, reduce the time of transient processes by 3–5 times, reduce the variance of errors by 2.7 times, and reduce the sensitivity of the system to the change of object parameters compared to typical regulators.

Keywords: discrete-continuous plant, nonlinear robust control, Hamilton-Jacobi-Isaacs equation, multicriteria parametric optimization, stochastic metaheuristic optimization algorithm.

Full text: Download in PDF

References

1. Jin, M., Kang, S. H., & Chang, P. H. (2008). Robust compliant motion control of robot with nonlinear friction using time-delay estimation. IEEE Transactions on Industrial Electronics, vol. 55, iss. 1, pp. 258–269. https://doi.org/10.1109/TIE.2007.906132.
2. Marton, L. & Lantos, B. (2007). Modeling, identification, and compensation of stick-slip friction. IEEE Transactions on Industrial Electronics, vol. 54, iss. 1, pp. 511–521. https://doi.org/10.1109/TIE.2006.888804.
3. Sushchenko, O., Averyanova, Yu., Ostroumov, I., Kuzmenko, N., Zaliskyi, M., Solomentsev, O., Kuznetsov, B., Nikitina, T., Havrylenko, O., Popov, A., Volosyuk, V., Shmatko, O., Ruzhentsev, N., Zhyla, S., Pavlikov, V., Dergachov, K., & Tserne, E. (2022). Algorithms for design of robust stabilization systems. In: Gervasi, O., Murgante, B., Hendrix, E. M. T., Taniar, D., Apduhan, B. O. (eds.) Computational Science and Its Applications – ICCSA 2022. Lecture Notes in Computer Science, vol. 13375. Cham: Springer, pp. 198–213. https://doi.org/10.1007/978-3-031-10522-7_15.
4. Shmatko, O., Volosyuk, V., Zhyla, S., Pavlikov, V., Ruzhentsev, N., Tserne, E., Popov, A., Ostroumov, I., Kuzmenko, N., Dergachov, K., Sushchenko, O., Averyanova, Yu., Zaliskyi, M., Solomentsev, O., Havrylenko, O., Kuznetsov, B., & Nikitina, T. (2021). Synthesis of the optimal algorithm and structure of contactless optical device for estimating the parameters of statistically uneven surfaces. Radioelectronic and Computer Systems, no. 4, pp. 199–213. https://doi.org/10.32620/reks.2021.4.16.
5. Volosyuk, V., Zhyla, S., Pavlikov, V., Ruzhentsev, N., Tserne, E., Popov, A., Shmatko, O., Dergachov, K., Havrylenko, O., Ostroumov, I., Kuzmenko, N., Sushchenko, O., Averyanova, Yu., Zaliskyi, M., Solomentsev, O., Kuznetsov, B., & Nikitina, T. (2022). Optimal method for polarization selection of stationary objects against the background of the Earth’s surface. International Journal of Electronics and Telecommunications, vol. 68, no. 1, pp. 83–89. https://doi.org/10.24425/ijet.2022.139852.
6. Ostroumov, I., Kuzmenko, N., Sushchenko, O., Pavlikov, V., Zhyla, S., Solomentsev, O., Zaliskyi, M., Averyanova, Yu., Tserne, E., Popov, A., Volosyuk, V., Ruzhentsev, N., Dergachov, K., Havrylenko, O., Kuznetsov, B., Nikitina, T., & Shmatko, O. (2021). Modelling and simulation of DME navigation global service volume. Advances in Space Research, vol. 68, iss. 8, pp. 3495–3507. https://doi.org/10.1016/j.asr.2021.06.027.
7. Averyanova, Yu., Sushchenko, O., Ostroumov, I., Kuzmenko, N., Zaliskyi, M., Solomentsev, O., Kuznetsov, B., Nikitina, T., Havrylenko, O., Popov, A., Volosyuk, V., Shmatko, O., Ruzhentsev, N., Zhyla, S., Pavlikov, V., Dergachov, K., & Tserne, E. (2021). UAS cyber security hazards analysis and approach to qualitative assessment. In: Shukla, S., Unal, A., Varghese Kureethara, J., Mishra, D. K., & Han, D. S. (eds) Data Science and Security. Lecture Notes in Networks and Systems, vol. 290, pp. 258–265. https://doi.org/10.1007/978-981-16-4486-3_28.
8. Zaliskyi, M., Solomentsev, O., Shcherbyna, O., Ostroumov, I., Sushchenko, O., Averyanova, Yu., Kuzmenko, N., Shmatko, O., Ruzhentsev, N., Popov, A., Zhyla, S., Volosyuk, V., Havrylenko, O., Pavlikov, V., Dergachov, K., Tserne, E., Nikitina, T., & Kuznetsov, B. (2021). Heteroskedasticity analysis during operational data processing of radio electronic systems. In: Shukla, S., Unal, A., Varghese Kureethara, J., Mishra, D. K., & Han, D. S. (eds.) Data Science and Security. Lecture Notes in Networks and Systems, vol. 290, pp. 168–175. https://doi.org/10.1007/978-981-16-4486-3_18.
9. Ostroumov, I., Kuzmenko, N., Sushchenko, O., Zaliskyi, M., Solomentsev, O., Averyanova, Yu., Zhyla, S., Pavlikov, V., Tserne, E., Volosyuk, V., Dergachov, K., Havrylenko, O., Shmatko, O., Popov, A., Ruzhentsev, N., Kuznetsov, B., & Nikitina, T. (2021). A probability estimation of aircraft departures and arrivals delays. In: Gervasi, O. et al. (eds.) Computational Science and Its Applications (ICCSA 2021). Lecture Notes in Computer Science, vol. 12950, pp. 363–377. https://doi.org/10.1007/978-3-030-86960-1_26.
10. Zhyla, S., Volosyuk, V., Pavlikov, V., Ruzhentsev, N., Tserne, E., Popov, A., Shmatko, O., Havrylenko, O., Kuzmenko, N., Dergachov, K., Averyanova, Yu., Sushchenko, O., Zaliskyi, M., Solomentsev, O., Ostroumov, I., Kuznetsov, B., & Nikitina, T. (2022). Statistical synthesis of aerospace radars structure with optimal spatio-temporal signal processing, extended observation area and high spatial resolution. Radioelectronic and Computer Systems, no. 1, pp. 178–194. https://doi.org/10.32620/reks.2022.1.14.
11. Maksymenko-Sheiko, K. V., Sheiko, T. I., Lisin, D. O., & Petrenko, N. D. (2022). Mathematical and computer modeling of the forms of multi-zone fuel elements with plates. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 25, no. 4, pp. 32–38. https://doi.org/10.15407/pmach2022.04.032.
12. Hontarovskyi, P. P., Smetankina, N. V., Ugrimov, S. V., Garmash, N. H., & Melezhyk, I. I. (2022). Computational studies of the thermal stress state of multilayer glazing with electric heating. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 25, no. 2, pp. 14–21. https://doi.org/10.15407/pmach2022.02.014.
13. Kostikov, A. O., Zevin, L. I., Krol, H. H., & Vorontsova, A. L. (2022). The optimal correcting the power value of a nuclear power plant power unit reactor in the event of equipment failures. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 25, no. 3, pp. 40–45. https://doi.org/10.15407/pmach2022.03.040.
14. Rusanov, A. V., Subotin, V. N., Khoryev, O. M., Bykov, Yu. A., Korotaiev, P. O., & Ahibalov, Ye. S. (2022). Effect of 3D shape of pump-turbine runner blade on flow characteristics in turbine mode. Journal of Mechanical Engineering – Problemy Mashynobuduvannia, vol. 25, no. 4, pp. 6–14. https://doi.org/10.15407/pmach2022.04.006.
15. Hashim, F. A., Hussain, K., Houssein, E. H., Mabrouk, M. S., & Al-Atabany, W. (2021). Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems. Applied Intelligence, vol. 51, pp. 1531–1551. https://doi.org/10.1007/s10489-020-01893-z.

Received 19 February 2024

Published 30 September 2024