Email this article BACKSTEPPING STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS UNDER STATE CONSTRAINTS
- Authors: Golubev A.E.1
-
Affiliations:
- Ishlinsky Institute for Problems in Mechanics of RAS
- Issue: Vol 60, No 5 (2024)
- Pages: 660–671
- Section: CONTROL THEORY
- URL: https://journals.rcsi.science/0374-0641/article/view/259936
- DOI: https://doi.org/10.31857/S0374064124050074
- EDN: https://elibrary.ru/LBJSHT
- ID: 259936
Cite item
Open Access
Access granted
Subscription Access
Abstract
The problem of stabilizing the zero value of the state vector of constrained nonlinear dynamical systems written in a special form is solved. The proposed control design accounts for magnitude constraints on the values of state variables and is based on the integrator backstepping approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in contrast to similar known results, are based on the use of linear virtual stabilizing functions that do not grow unbounded as state variables approach the boundary values. As an example, we consider a state constraints aware solution to the control problem of positioning an autonomous underwater vehicle at a given point in space.
About the authors
A. E. Golubev
Ishlinsky Institute for Problems in Mechanics of RAS
Email: v-algolu@hotmail.com
Moscow, Russia
References
- Krsti´c, M. Nonlinear and Adaptive Control Design / M. Krsti´c, I. Kanellakopoulos, P.V. Kokotovi´c. — New York : John Wiley and Sons, 1995. — 592 p.
- Ngo, K.B. Integrator backstepping using barrier functions for systems with multiple state constraints / K.B. Ngo, R. Mahony, Z.P. Jiang // Proc. 44th IEEE Conference on Decision and Control, and the European Control Conference. — Seville, Spain, 2005. — P. 8306–8312.
- Tee, K.P. Barrier Lyapunov functions for the control of output-constrained nonlinear systems / K.P. Tee, S.S. Ge, E.H. Tay // Automatica. — 2009. — V. 45, № 4. — P. 918–927.
- Tang, Z.L. Tangent barrier Lyapunov functions for the control of output-constrained nonlinear systems / Z.L. Tang, K.P. Tee, W. He // IFAC Proceedings Volumes. — 2013. — V. 46, № 20. — P. 449–455.
- Niu, B. Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems / B. Niu, J. Zhao // Systems and Control Letters. — 2013. — V. 62, № 10. — P. 963–971.
- Xu, J. Adaptive finite-time fault-tolerant tracking control for a class of MIMO nonlinear systems with output constraints / J. Xu // Int. J. of Robust and Nonlin. Control. — 2017. — V. 27, № 5. — P. 722–741.
- Sachan, K. Barrier Lyapunov function based output-constrained control of nonlinear Euler–Lagrange systems / K. Sachan, R. Padhi // Proc. 15th Int. Conf. on Control, Automation, Robotics and Vision (ICARCV). — Singapore, 2018. — P. 686–691.
- Golubev, A.E. Backstepping control of aircraft take-off in windshear / A.E. Golubev, N.D. Botkin, A.P. Krishchenko // IFAC-PapersOnLine. — 2019. — V. 52, № 16. — P. 712–717.
- D UAV navigation with moving-obstacle avoidance using barrier Lyapunov functions / E. Restrepo, I. Sarras, A. Loria, J. Marzat // IFAC-PapersOnLine. — 2019. — V. 52, № 12. — P. 49–54.
- Garg, T. Barrier Lyapunov function based controller design for Euler-Lagrange systems with reduced control effort / T. Garg, S.B. Roy // IFAC-PapersOnLine. — 2020. — V. 53, № 1. — P. 459–464.
- Barrier Lyapunov function-based fixed-time FTC for high-order nonlinear systems with predefined tracking accuracy / X. Wang, J. Xu, M. Lv [et al.] // Nonlinear Dynamics. — 2022. — V. 110. — P. 381–394.
- Golubev, A. Modeling of cerebral blood flow autoregulation using mathematical control theory / A. Golubev, A. Kovtanyuk, R. Lampe // Mathematics. — 2022. — V. 10, № 12. — Art. 2060.
- Barrier Lyapunov function-based finite-time reliable trajectory tracking control of fixed-wing UAV with error constraints / Y. Xu, R. Zhou, Z. Yu [et al.] // IFAC-PapersOnLine. — 2022. — V. 55, № 6. — P. 597–602.
- Голубев, А.Е. Стабилизация программных движений механических систем с учётом ограничений / А.Е. Голубев // Изв. РАН. ТиСУ. — 2023. — № 4. — C. 153–167.
- Boyd, S. Convex Optimization / S. Boyd, L. Vandenberghe. — Cambridge : Cambridge University Press, 2009. — 699 p.
- Khalil, H.K. Nonlinear Systems. 3d ed. / H.K. Khalil. — Upper Saddle River, New Jersey : Prentice Hall, 2002. — 750 p.
- Fossen T.I. Guidance and Сontrol of Ocean Vehicles / T.I. Fossen. — Chichester : John Wiley and Sons, 1994. — 494 p.
- Silpa-Anan, C. Kambara: past, present, and future / C. Silpa-Anan, A. Zelinsky // Proc. 2001 Australian Conference on Robotics and Automation. — 2001. — P. 61–66.
- Isidori, A. Nonlinear Control Systems. 3rd ed. / A. Isidori. — London : Springer-Verlag, 1995. — 549 p.
- Краснощеченко, В.И. Нелинейные системы: геометрические методы анализа и синтеза / В.И. Краснощеченко, А.П. Крищенко. — М. : Изд-во МГТУ имени Н.Э. Баумана, 2005. — 519 с.
