Finite time stabilization of non-autonomous, nonlinear second-order systems based on minimum time principle
Author affiliations
DOI:
https://doi.org/10.15625/2525-2518/59/2/15679Keywords:
FTS, FINITE TIME STABILIZATIONAbstract
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
Downloads
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
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Vietnam Journal of Sciences and Technology (VJST) is an open access and peer-reviewed journal. All academic publications could be made free to read and downloaded for everyone. In addition, articles are published under term of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) Licence which permits use, distribution and reproduction in any medium, provided the original work is properly cited & ShareAlike terms followed.
Copyright on any research article published in VJST is retained by the respective author(s), without restrictions. Authors grant VAST Journals System a license to publish the article and identify itself as the original publisher. Upon author(s) by giving permission to VJST either via VJST journal portal or other channel to publish their research work in VJST agrees to all the terms and conditions of https://creativecommons.org/licenses/by-sa/4.0/ License and terms & condition set by VJST.
Authors have the responsibility of to secure all necessary copyright permissions for the use of 3rd-party materials in their manuscript.
Vietnam Journal of Science and Technology (VJST) is pleased to notice: