MACHINE LEARNING BASED ON SYMBOLIC REGRESSION FOR AUTOMATED SYNTHESIS OF UNIVERSAL MOTION STABILIZATION SYSTEMS
- Authors: Diveev A.I.1,2, Barabash A.D.1
-
Affiliations:
- Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
- People's Friendship University of Russia
- Issue: No 3 (2025)
- Pages: 5-16
- Section: FUNDAMENTALS OF RELIABILITY AND QUALITY ISSUES
- URL: https://journal-vniispk.ru/2307-4205/article/view/353660
- DOI: https://doi.org/10.21685/2307-4205-2025-3-1
- ID: 353660
Cite item
Full Text
Abstract
Background. This study considers an optimal control problem in an extended formulation, aimed at ensuring the feasibility of the solution under real-world operating conditions. Materials and methods. To achieve high accuracy and stability of the controlled plant's motion, it is proposed to synthesize a universal stabilization system capable of reliably following a wide range of trajectories, even in the presence of external influences and model uncertainties. The concept of an extended model of the controlled plant is presented, including both the plant itself with the stabilization system and a reference model for generating the optimal trajectory. It is shown that using such a structure, classical optimal control methods can be applied to obtain the control function as a function of time, achieving a high degree of conformity between the plant's motion and the planned trajectory while maintaining stability and control accuracy. To synthesize the universal stabilization system, machine learning based on symbolic regression is used, which allows for the formalization of the process of constructing control functions and eliminates the subjective errors typical of manual design. Results and conclusions. The effectiveness of the proposed approach is confirmed by a computational example of controlling the spatial motion of a group of quadcopters – a typical example of complex engineering systems with high requirements for reliability, maneuverability, and safety.
About the authors
Askhat I. Diveev
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences; People's Friendship University of Russia
Author for correspondence.
Email: aidiveev@mail.ru
Doctor of technical sciences, professor, chief researcher, head of department 55, Director of the Robot Center; professor of the department of mechanics and mechatronics
40 Vavilov street, Moscow, Russia; 3 Ordzhonikidze street, Moscow, RussiaArtem D. Barabash
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
Email: artew44@gmail.com
Postgraduate student
40 Vavilov street, Moscow, RussiaReferences
- Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimal′nykh protsessov = Mathematical theory of optimal processes. New York; London; Parizh; Montre; Tokio: Gordon and Breach Science Publishers, 1985;4:360. (In Russ.)
- Godunov A.I., Yerofeyev M.V., Mel′nichuk A.I. et al. Information field of detection of small-sized unmanned aerial vehicles in space based on neural networks. Nadezhnost′ i kachestvo slozhnykh system = Reliability and quality of complex systems. 2024;(4):5–14. (In Russ.)
- Voronin E.A. Application of machine learning technologies in the tasks of assessing and ensuring the reliability of technical systems, taking into account the safety of their operation. Nadezhnost′ i kachestvo slozhnykh system = Reliability and quality of complex systems. 2024;(4):75–84. (In Russ.)
- Diveev A. Refined Optimal Control Problem and Its Solution Using Symbolic Regression. Lecture Notes in Networks and Systems. 2022;507:294–305.
- Diveev A., Barabash A. The Extended Optimal Control Problem and Numerical Techniques of its Solving. Proceedings of 2023 9th International Conference on Control, Decision and Information Technologies (CoDIT). Rome, Italy, 2023.
- Samir A., Hammad A., Hafez A., Mansour H. Quadcopter Trajectory Tracking Control using State-Feedback Control with Integral Action. International Journal of Computer Applications. 2017;168:1–7.
- Walsh G., Tilbury D., Sastry S. et al. Stabilization of trajectories for systems with nonholonomic constraints. IEEE Transactions on Automatic Control. 1994;39:216–222.
- Uddin N. A Robot Trajectory Tracking Control System Design Using Pole Domination Approach. Proceedings of IEEE 9th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON). Vancouver, Canada, 2018:506–512.
- Pamosoaji A.K. Trajectory Tracking Control Strategy using Co-Reference for Rear-Steered Vehicle. Proceedings of 3rd International Conference on Control and Robotics Engineering (ICCRE). Nagoya, Japan, 2018:74–78.
- Andreev A., Peregudova O., Sutyrkina K., Filatkina E. On Global Output Feedback Trajectory Tracking Control of a Wheeled Mobile Robot. Proceedings of 23rd International Conference on Mechatronics Technology (ICMT). Salerno, Italy, 2019:1–5.
- Yu X., Zhu W., Xu L. Real-time Motion Planning and Trajectory Tracking in Complex Environments based on Bezier Curves and Nonlinear MPC Controller. Proceedings of the Chinese Control and Decision Conference (CCDC). Hefei, China, 2020:1540–1546.
- Zhao H., Su G., Yang. Anti-collision Trajectory Planning and Tracking Control based on MPC and Fuzzy PID Algorithm. Proceedings of the 2020 4th CAA International Conference on Vehicular Control and Intelligence (CVCI). Hangzhou, China, 2020:613–618.
- Su T., Liang X., He G. et al. Robust Trajectory Tracking of Delta Parallel Robot Using Sliding Mode Control. Proceedings of the IEEE Symposium Series on Computational Intelligence (SSCI). Xiamen, China, 2019:508–512.
- Koza J.R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, 1992:819.
- Diveev A.I., Shmalko E.Yu. Machine Learning Control by Symbolic Regression. Springer, Cham, Switzerland, 2021:156.
- Diveev A.I. Hybrid Evolutionary Algorithm for Optimal Control Problem. Lecture Notes in Networks and Systems. 2023;543 LNNS:726–738.
Supplementary files
