Geodesic
On the finite time stabilization via robust control for uncertain disturbed systems
International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 1, pp. 71-82.

Voir la notice de l'article provenant de la source Library of Science

This paper deals with the finite-time stabilization problem for a class of uncertain disturbed systems using linear robust control. The proposed algorithm is designed to provide the robustness of a linear feedback control scheme such that system trajectories arrive at a small-size attractive set around an unstable equilibrium in a finite time. To this end, an optimization problem with a linear matrix inequality constraint is presented. This means that the effects of external disturbances, as well as matched and mismatched uncertain dynamics, can be significantly reduced. Finally, the performance of the suggested closed-loop control strategies is shown by the trajectory tracking of an unmanned aerial vehicle flight.
Keywords: finite time bounded stability, uncertain disturbed system, robust stabilization, ultimate bound minimization
Mots-clés : stabilność ograniczona, układ niepewny, stabilizacja odporna, minimalizacja ograniczona 
@article{IJAMCS_2023_33_1_a5,
     author = {Ordaz, Patricio and Alazki, Hussain and S\'anchez, Bonifacio and Ordaz-Oliver, Mario},
     title = {On the finite time stabilization via robust control for uncertain disturbed systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {71--82},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_1_a5/}
}
TY  - JOUR
AU  - Ordaz, Patricio
AU  - Alazki, Hussain
AU  - Sánchez, Bonifacio
AU  - Ordaz-Oliver, Mario
TI  - On the finite time stabilization via robust control for uncertain disturbed systems
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2023
SP  - 71
EP  - 82
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_1_a5/
LA  - en
ID  - IJAMCS_2023_33_1_a5
ER  - 
%0 Journal Article
%A Ordaz, Patricio
%A Alazki, Hussain
%A Sánchez, Bonifacio
%A Ordaz-Oliver, Mario
%T On the finite time stabilization via robust control for uncertain disturbed systems
%J International Journal of Applied Mathematics and Computer Science
%D 2023
%P 71-82
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_1_a5/
%G en
%F IJAMCS_2023_33_1_a5
Ordaz, Patricio; Alazki, Hussain; Sánchez, Bonifacio; Ordaz-Oliver, Mario. On the finite time stabilization via robust control for uncertain disturbed systems. International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 1, pp. 71-82. http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_1_a5/

[1] [1] Amato, F., Ambrosino, R., Ariola, M., Cosentino, C., De Tommasi, G. (2014). Finite-Time Stability and Control, Springer, London.

[2] [2] Amato, F., Ariola, M., Cosentino, C., Abdallah, C. and Dorato, P. (2003). Necessary and sufficient conditions for finite-time stability of linear systems, Proceedings of the 2003 American Control Conference, Denver, USA, Vol. 5, pp. 4452-4456.

[3] [3] Amato, F., Ariola, M. and Dorato, P. (2001). Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica 37(9): 1459-1463.

[4] [4] Bhat, S.P. and Bernstein, D.S. (2000). Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization 38(3): 751-766.

[5] [5] Edwards, C. and Spurgeon, S. (1998). Sliding Mode Control: Theory and Applications, CRC Press, Boca Raton.

[6] [6] Haddad, W.M. and Chellaboina, V. (2011). Nonlinear Dynamical Systems and Control: A Lyapunov-based Approach, Princeton University Press, Princeton.

[7] [7] Khalil, H.K. and Grizzle, J.W. (2002). Nonlinear Systems, Vol. 3, Prentice Hall, Upper Saddle River.

[8] [8] Kokotović, P.V., Nicosia, T., Menini, L., Zaccarian, L. and Abdallah, C.T. (2006). Current Trends in Nonlinear Systems and Control: In Honor of Petar Kokotovic and Turi Nicosia, Springer, Boston.

[9] [9] Kukurowski, N., Mrugalski, M., Pazera, M. and Witczak, M. (2022). Fault-tolerant tracking control for a non-linear twin-rotor system under ellipsoidal bounding, International Journal of Applied Mathematics and Computer Science 32(2): 171-183, DOI: 10.34768/amcs-2022-0013.

[10] [10] Li, X., Ho, D.W. and Cao, J. (2019). Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica 99: 361-368.

[11] [11] Liu, H., Zhong, M. and Yang, R. (2018). Simultaneous disturbance compensation and Hi/H∞ optimization in fault detection of UAVs, International Journal of Applied Mathematics and Computer Science 28(2): 349-362, DOI: 10.2478/amcs-2018-0026.

[12] [12] Orlov, Y., Aoustin, Y. and Chevallereau, C. (2010). Finite time stabilization of a perturbed double integrator. Part I: Continuous sliding mode-based output feedback synthesis, IEEE Transactions on Automatic Control 56(3): 614-618.

[13] [13] Polyakov, A., Efimov, D. and Perruquetti, W. (2015). Finite-time and fixed-time stabilization: Implicit Lyapunov function approach, Automatica 51: 332-340.

[14] [14] Poznyak, A., Polyakov, A. and Azhmyakov, V. (2014). Attractive Ellipsoids in Robust Control, Springer, Cham.

[15] [15] Puangmalai, J., Tongkum, J. and Rojsiraphisal, T. (2020). Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality, Mathematics and Computers in Simulation 171: 170-186.

[16] [16] Utkin, V.I. and Poznyak, A.S. (2013). Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method, Automatica 49(1): 39-47.

[17] [17] Wang, H., Liu, P.X., Zhao, X. and Liu, X. (2019). Adaptive fuzzy finite-time control of nonlinear systems with actuator faults, IEEE Transactions on Cybernetics 50(5): 1786-1797.

[18] [18] Weiss, L. and Infante, E. (1967). Finite time stability under perturbing forces and on product spaces, IEEE Transactions on Automatic Control 12(1): 54-59.

[19] [19] Yu, S., Yu, X., Shirinzadeh, B. and Man, Z. (2005). Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica 41(11): 1957-1964.