Stabilization of Programmed Motions of Constrained Mechanical Systems

A. E. Golubev; Голубев А. Е.

doi:10.31857/S0002338823040054

Stabilization of Programmed Motions of Constrained Mechanical Systems

Authors: Golubev A.E.¹
Affiliations:
1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences (IPMech RAS), 119526, Moscow, Russia
Issue: No 4 (2023)
Pages: 153-167
Section: CONTROL SYSTEMS FOR MOVING OBJECTS
URL: https://rjmseer.com/0002-3388/article/view/676481
DOI: https://doi.org/10.31857/S0002338823040054
EDN: https://elibrary.ru/OCLSAO
ID: 676481

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Abstract
About the authors
References
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Abstract

The problem of the stabilization of programmed trajectories of mechanical systems, taking the constraints on the values of generalized coordinates, velocities, and accelerations into account, is considered. The control is built using the backstepping method in combination with the use of logarithmic Lyapunov barrier functions. The stabilizing feedbacks obtained in this study, in contrast to similar known results, do not lead to an unlimited increase in the values of the control variables when the state variables of the system approach the boundary values. As an example, the problem of constructing and stabilizing the trajectory of the spatial motion of an underwater vehicle is considered.

About the authors

A. E. Golubev

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences (IPMech RAS), 119526, Moscow, Russia

Author for correspondence.
Email: v-algolu@hotmail.com
Россия, Москва

References

Olfati-Saber R. Flocking for Multi-agent Dynamic Systems: Algorithms and Theory // IEEE Trans. Automat. Contr. 2006. V. 51 (3). P. 401–420.
Liu H., Chen G., Tian X. Cooperative Formation Control for Multiple Surface Vessels Based on Barrier Lyapunov Function and Self-structuring Neural Networks // Ocean Engineering. 2020. V. 216. 108163.
Крутько П.Д. Обратные задачи динамики управляемых систем. Нелинейные модели. М.: Наука, 1988. 326 с.
Isidori A. Nonlinear Control Systems. 3rd ed. London: Springer-Verlag, 1995. 549 p.
Краснощеченко В.И., Крищенко А.П. Нелинейные системы: геометрические методы анализа и синтеза. М.: Изд-во МГТУ им. Н.Э. Баумана, 2005. 520 с.
Krstić M., Kanellakopoulos I., Kokotović P.V. Nonlinear and Adaptive Control Design. New York: John Wiley and Sons, 1995. 563 p.
Ortega R., Loria A., Nicklasson P.J., Sira-Ramirez H. Passivity-based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. London: Springer-Verlag, 1998. 543 p.
Ngo K.B., Mahony R., Jiang Z.P. Integrator Backstepping Using Barrier Functions for Systems with Multiple State Constraints // Proc. 44th IEEE Conf. on Decision and Control, and the European Control Conf. Seville, Spain, 2005. P. 8306–8312.
Tee K.P., Ge S.S., Tay E.H. Barrier Lyapunov Functions for the Control of Output-constrained Nonlinear Systems // Automatica. 2009. V. 45 (4). P. 918–927.
Boyd S., Vandenberghe L. Convex Optimization. Cambridge: University Press, 2009. 716 p.
Niu B., Zhao J. Barrier Lyapunov Functions for the Output Tracking Control of Constrained Nonlinear Switched Systems // Systems and Control Letters. 2013. V. 62 (10). P. 963–971.
Sachan K., Padhi R. Barrier Lyapunov Function Based Output-constrained Control of Nonlinear Euler-Lagrange Systems // Proc. 15th Intern. Conf. on Control, Automation, Robotics and Vision (ICARCV). Singapore, 2018. P. 686–691.
Golubev A.E., Botkin N.D., Krishchenko A.P. Backstepping Control of Aircraft Take-off in Windshear // IFAC-PapersOnLine. 2019. V. 52 (16). P. 712–717.
Garg T., Roy S.B. Barrier Lyapunov Function Based Controller Design for Euler-Lagrange Systems with Reduced Control Effort // IFAC-PapersOnLine. 2020. V. 53 (1). P. 459–464.
Wang X., Xu J., Lv M., Zhang L., Zhao Z. Barrier Lyapunov Function-based Fixed-time FTC for High-order Nonlinear Systems with Predefined Tracking Accuracy // Nonlinear Dynamics. 2022. V. 110. P. 381–394.
Golubev A., Kovtanyuk A., Lampe R. Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory // Mathematics. 2022. V. 10 (12). 2060.
Голубев А.Е. Построение программных движений механических систем с учетом ограничений при помощи многочленов третьего порядка // Изв. РАН. ТиСУ. 2021. № 2. С. 126–137.
Sussmann H.J., Kokotovic P.V. The Peaking Phenomenon and the Global Stabilization of Nonlinear Systems // IEEE Transactions on Automatic Control. 1991. V. 36 (4). P. 424–440.
Khalil H.K. Nonlinear Systems. 3rd ed. Upper Saddle River: Prentice Hall, 2002.
Fossen T.I. Guidance and Control of Ocean Vehicles. Chichester: John Wiley and Sons, 1994.
Silpa-Anan C., Zelinsky A. Kambara: Past, Present, and Future // Proc. 2001 Australian Conf. on Robotics and Automation. Sydney, 2001. P. 61–66.
Silpa-Anan C. Autonomous Underwater Robot: Vision and Control. Master thesis. Canberra: Australian National University, 2001. https://doi.org/10.25911/5d626dd9b96ec.