NEURAL NETWORK APPROXIMATION OF MODEL-PREDICTIVE CONTROL FOR A DYNAMIC OBJECT STABILIZATION SYSTEM
Abstract
Relevance. When solving problems of stabilization of dynamic objects, classical model predictive control is widely used. It provides high quality control by solving the optimization problem at each step, but it has significant computing costs, which limits its application in real-time systems with high requirements for update frequency. Therefore, the question of investigating the applicability of a neural network regulator trained on a model predictive regulator (MPC) when solving the problem of stabilizing the position of a dynamic object with a limited computational and time resource is relevant. Goal. The purpose of the presented work was to develop and study a neural network regulator trained on the basis of an MPC regulator to stabilize the position of a dynamic object on a mobile platform. Methods. When performing the work, methods of system analysis, simulation modeling, as well as experimental tests on the bench were used. Results and conclusions. As part of the study, a neural network regulator was developed and trained that approximates the behavior of MPC based on data obtained when controlling a real balancing platform. The training was conducted on the input and output data of the MPC without using the internal model of the system, which made it possible to reproduce the dynamics of the regulator at significantly lower computational costs. Experimental results showed that the neural network model provides a stabilization quality comparable to the original MPC, while the calculation time was reduced from 47 ms to 1.6 ms, which amounted to an acceleration value of 29 times. The proposed approach demonstrates the potential of neural network control methods in the problems of replacing complex optimization regulators for systems with limited computing resources.
References
1. Afonin V.V., Muryumin S.M. Obratnye zadachi optimal'noy stabilizatsii so skalyarnym upravleniem [In-verse problems of optimal stabilization with scalar control], Vestnik Mordovskogo universiteta [Bulletin of the Mordovian University], 2017, Vol. 27, No. 4, pp. 504-517. DOI: 10.15507/0236-2910.027.201704.504-517.
2. Yaseen M.G., Aljanabi M. Recent Advances in Control Theory for Complex Systems, Babylonian Jour-nal of Mathematics, 2023, pp. 7-11.
3. Golubev A.E. Stabilizatsiya programmnykh dvizheniy mekhanicheskikh sistem s uchetom ogranicheniy [Stabilization of program movements of mechanical systems, taking into account restrictions], Izvestiya RAN. Teoriya i sistemy upravleniya [Izvestia RAS. Theory and control systems], 2023, No. 4, pp. 153-167.
4. Schwenzer M., Ay M., Bergs T., Abel D. Review on Model Predictive Control: An Engineering Perspec-tive, The International Journal of Advanced Manufacturing Technology, 2021, Vol. 117,
pp. 1327-1349. DOI: 10.1007/s00170-021-07682-3.
5. Senthil Kumar Arumugasamy, Zainal Ahmad. Model Predictive. Control (MPC) and Its Current Issues in Chemical Engineering, Chemical Engineering Communications, 2012, 199 (4), pp. 472-511. DOI: 10.1080/00986445.2011.592446.
6. Shevlyagin S.A., Torgashov A.Yu. Upravlenie tekhnologicheskimi protsessami na osnove prognoziruyushchikh modeley: ucheb. posobie dlya vuzov [Process management based on predictive models: a textbook for universities]. Vladivostok: Izd-vo Dal'nevost. federal. un-ta, 2024, 84 p.
7. Lepikhin T.A. Metody povysheniya bystrodeystviya tsifrovykh sistem s lineynoy obratnoy svyaz'yu [Methods for increasing the speed of digital systems with linear feedback], Vestnik Sankt-Peterburgskogo universiteta. Seriya 10: Prikladnaya matematika. Informatika. Protsessy upravleniya [Bulletin of St. Petersburg University. Series 10: Applied Mathematics. Computer science. Management processes], 2010, No. 4, pp. 96-108.
8. McAllister R., Chua K., Calandra R. and Levine S. Deep reinforcement learning in a handful of trials using probabilistic dynamics models, In Advances in Neural Information Processing Systems, 2018, pp. 4754-4765.
9. Khajanchi H.I., Bruno J.N., Adegbege A.A. An Embedded FPGA Architecture for Real Time Model Predictive Control, IFAC PapersOnLine, 2020, Vol. 53 (2), pp. 7833-7838. DOI: 10.1016/ j.ifacol.2020.12.1886
10. Zhang X., Bujarbaruah M., Borrelli F. Near-Optimal Rapid MPC Using Neural Networks: A Primal-Dual Policy Learning Framework, IEEE Transactions on Control Systems Technology, pp. 1-13. DOI: 10.1109/TCST.2020.3024571.
11. Alsmeier H., Theiner L., Savchenko A., Mesbah A., Findeisen R. Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification, IEEE 63rd Conference on Decision and Control, 2024, pp. 4777-4782. DOI: 10.48550/arXiv.2501.03671.
12. Gonzalez C., Asadi H., Kooijman L., Lim C.P. Neural Networks for Fast Optimisation in Model Predic-tive Control: A Review, CoRR, 2023. DOI: 10.48550/ARXIV.2309.02668.
13. Curtis C., Quackenbush T., Sorensen T., Wingate D., Killpack M.D. Using First Principles for Deep Learning and Model-Based Control of Soft Robots, Frontiers in Robotics and AI, 2021, Vol. 8, Article 654398. DOI: 10.3389/frobt.2021.654398.
14. Karg B., Lucia S. Efficient Representation and Approximation of Model Predictive Control Laws via Deep Learning, IEEE Transactions on Cybernetics, 2020, Vol. 50, No. 9, pp. 3866-3878. DOI: 10.1109/TCYB.2020.2999556.
15. Phuong T.H., Belov M.P., Tran D.K. Model predictive controller based on Laguerre functions for larg-eradio telescope servo control system, IEEE Conf. El-ConRusNW, SPb., 2018, pp. 1020-1024.
16. Belov M.P., Fyong Ch.Kh., Tkhuy D.V. Adaptivnoe prognoziruyushchee upravlenie sledyashchimi el-ektroprivodami nelineynykh sistem s uprugimi svyazyami [Adaptive predictive control of tracking elec-tric drives of non-linear systems with elastic bonds], Izvestiya SPbGETU «LETI» [Izvestia SPbGETU «LETI»], 2019, No. 3, pp. 84-94.
17. Filimonov A.B., Filimonov N.B. Synthesis of Servo-systems on the Basis of the Apparatus of Linear-Quadratic Optimization, Mekhatronika, avtomatizatsiya, upravlenie, 2016, Vol. 17, No. 12, pp. 795-801. DOI: 10.17587/mau.17.795-801.
18. He Z., Wu J., Zhang J., Zhang S., Shi Y., Liu H., Sun L., Su Y., Leng X. CDM-MPC: An Integrated Dynamic Planning and Control Framework for Bipedal Robots Jumping, IEEE Robotics and Automa-tion Letters, 2024, Vol. 9, pp. 6672-6679. DOI: 10.1109/LRA.2024.3408487.
19. Ali A.M., Sha’aban Y.A., Salawudeen A.T., Haruna Z., Muhammad B., Mu’azu M.B., Alharthi A. Opti-mized Model Predictive Control for Improving Dynamic Stability and Steering Accuracy in Multi-Axle Cranes, PLoS One, 2025, Vol. 20. DOI: 10.1371/journal.pone.0324720.
20. Hou B., Yin Z., Jin X., Fan Z., Wang H. MPC-Based Dynamic Trajectory Spoofing for UAVs, Drones, 2024, Vol. 8, No. 10, pp. 602. DOI: 10.3390/drones8100602.
21. Tomás L., Lämmle M., Pfafferott J. Demonstration and Evaluation of Model Predictive Control (MPC) for a Real-World Heat Pump System in a Commercial Low-Energy Building for Cost Reduction and Enhanced Grid Support, Energies, 2025, Vol. 18, No. 6, pp 1434. DOI: 10.3390/en18061434.
22. Wang H., Liu B., Ping X., An Q. Path-Tracking Control for Autonomous Vehicles Based on an Im-proved MPC, IEEE Access, 2019, Vol. 7, pp. 161064-161073. DOI: 10.1109/ACCESS.2019.2944894.
23. Song H., Yue M., Qi G., Cai L., Zhao X. Longitudinal and Yaw Stability Control of Distributed Drive Vehicles Under Low Adhesion Conditions Based on MPC and Trigger Mechanism, Journal of Vibra-tion and Control, 2025, Vol. 0, No. 0, pp. 1-17. DOI: 10.1177/10775463251332835.
24. Wang Y., Sun K., Zhang W., Jin X. A Velocity-Adaptive MPC-Based Path Tracking Method for Heavy-Duty Forklift AGVs, Machines, 2024, Vol. 12, pp. 558. DOI: 10.3390/machines12080558.
25. Benotsmane R., Kovács G. Optimization of Energy Consumption of Industrial Robots Using Classical PID and MPC Controllers, Energies, 2023, Vol. 16, pp. 3499. DOI: 10.3390/en16083499.
