Finite time stabilization of non-autonomous, nonlinear second-order systems based on minimum time principle

Dang Van My, Trinh Hoang Minh, Vu Thi Thuy Nga, Nguyen Doan Phuoc
Author affiliations

Authors

  • Dang Van My Hanoi University of Science and Technology,1 Dai Co Viet Road, Ha Noi, Viet Nam
  • Trinh Hoang Minh Hanoi University of Science and Technology,1 Dai Co Viet Road, Ha Noi, Viet Nam
  • Vu Thi Thuy Nga Hanoi University of Science and Technology, 1 Dai Co Viet Road, Ha Noi, Viet Nam
  • Nguyen Doan Phuoc Hanoi University of Science and Technology,1 Dai Co Viet Road, Ha Noi, Viet Nam

DOI:

https://doi.org/10.15625/2525-2518/59/2/15679

Keywords:

FTS, FINITE TIME STABILIZATION

Abstract

This paper proposes a controller design method to stabilize a class of nonlinear, non-autonomous second-order systems in finite time. This method is developed based on exact-linearization and Pontryagin’s minimum time principle. It is shown that the system can be stabilized in a finite time of which the upper bound can be chosen according to the initial states of the system. Simulation results are given to validate the theoretical analysis

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References

Bhat,S.P. and Bernstein,D.S. – Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, 38(3) (2000), pp. 751–766. DOI: https://doi.org/10.1137/S0363012997321358

Hong,Y. – Finite-time stabilization and stabilizability of a class of controllable systems, Systems & control letters, 46(4) (2002), pp. 231–236. DOI: https://doi.org/10.1016/S0167-6911(02)00119-6

Moulay,E. and Perruquetti,W. – Lyapunov-based approach for finite time stability and stabilization, Proceedings of the 44th IEEE Conference on Decision and Control (2005). pp. 4742–4747.

Polyakov,A. – Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Transactions on Automatic Control, 57(8) (2011), pp. 2106–2110. DOI: https://doi.org/10.1109/TAC.2011.2179869

Pal,A.K., Kamal,S., Nagar,S.K., Bandyopadhyay,B. and Fridman,L. – Design of controllers with arbitrary convergence time, Automatica, 112 (2020). DOI: https://doi.org/10.1016/j.automatica.2019.108710

Basin,M. – Finite-and fixed-time convergent algorithms: Design and convergence time estimation’, Annual Reviews in Control (2019). DOI: https://doi.org/10.1016/j.arcontrol.2019.05.007

Venkataraman,S.T. and Gulati,S. – Control of nonlinear systems using terminal sliding modes, Proc. of the American Control Conference (ACC) (1993), pp. 891–893. DOI: https://doi.org/10.23919/ACC.1992.4792209

Levant,A. – Higher-order sliding modes, differentiation and output-feedback control, International Journal of Control, 76(9-10) (2003), pp. 924–941. DOI: https://doi.org/10.1080/0020717031000099029

Utkin,V. – About second order sliding mode control, relative degree, finite-time convergence and disturbance rejection (2010), 11th International Workshop on Variable Structure Systems (VSS), 2010. pp. 528–533 DOI: https://doi.org/10.1109/VSS.2010.5545133

Pontryagin,L.S., Boltjanskij,V.G., Gamkrelidze,R.V. and Miscenko,E.P. – Mathematische Theorie optimaler Prozesse, VEB Verlag Technik Berlin, 1964.

Brockett,R.W., Millman,R.S. and Sussmann,H.J. – Differential geometric control theory, Proceedings of the conference held at Michigan Technological University, June 28-July 2, vol. 27. (1983).

Isidori,A. – Nonlinear control systems, Volume ii’, Springer-Verlag, New York, 1999 DOI: https://doi.org/10.1007/978-1-4471-0549-7

Charlet,B., Lévine,J. and Marino,R. – On dynamic feedback linearization, Systems & Control Letters 13(2) (1989), pp. 143–151. DOI: https://doi.org/10.1016/0167-6911(89)90031-5

Shen,Z. and Andersson,S.B. – Minimum time control of a second-order system, 49th IEEE Conference on Decision and Control (CDC) (2010), pp. 4819–4824. DOI: https://doi.org/10.1109/CDC.2010.5717016

Shen,Z., Huang,P. and Andersson,S.B. – Calculating switching times for the time optimal control of single-input, single-output second-order systems, Automatica 49(5) (2013), pp. 1340–1347. DOI: https://doi.org/10.1016/j.automatica.2013.02.028

Schwarzgruber,T., Colaneri,P. and del Re,L. – Minimum-time control of a class of nonlinear systems with partly unknown dynamics and constrained input, IFAC Proceedings Volumes 46(23) (2013), pp. 211–216. DOI: https://doi.org/10.3182/20130904-3-FR-2041.00152

Vu,T.T.N. and Nguyen,D.P. – Finite time stabilization via time minimum principle (in vietnamese), J. of Science and Technology Thai Nguyen University 135(5) (2015).

Fenga,Y., Yub,X. and Man,Z. – Non-singular terminal sliding mode control of rigid manipulators, Automatica 38 (2002). pp. 2159–2167. DOI: https://doi.org/10.1016/S0005-1098(02)00147-4

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Published

16-03-2021

How to Cite

[1]
D. V. My, T. H. Minh, V. T. T. Nga, and N. D. Phuoc, “Finite time stabilization of non-autonomous, nonlinear second-order systems based on minimum time principle”, Vietnam J. Sci. Technol., vol. 59, no. 2, pp. 249–260, Mar. 2021.

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Electronics - Telecommunication