MACHINE LEARNING BASED ON SYMBOLIC REGRESSION
FOR AUTOMATED SYNTHESIS OF UNIVERSAL MOTION STABILIZATION SYSTEMS 

Askhat I. Diveev, Doctor of technical sciences, professor, chief researcher, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, head of department 55, Control of Robotic Devices; Director of the Robot Center of the FRC IU RAS, Computing Center named after A.A. Dorodnitsyn RAS (40 Vavilov street, Moscow, Russia); professor of the department of mechanics and mechatronics, Engineering Academy of the People's Friendship University of Russia (3 Ordzhonikidze street, Moscow, Russia), aidiveev@mail.ru
Artem D. Barabash, Postgraduate student, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences (40 Vavilov street, Moscow, Russia), artew44@gmail.com

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.

machine learning, symbolic regression, motion stabilization system, control, synthesis, model, optimal trajectory, control accuracy

Diveev A.I., Barabash A.D. Machine learning based on symbolic regression for automated synthesis of universal motion stabilization systems. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2025;(3):5–16. (In Russ.). doi: 10.21685/2307-4205-2025-3-1