Global finite-time output feedback stabilization for a class of uncertain nonholonomic systems. (English) Zbl 1421.93112

Du, Baojian; Gao, Fangzheng; Yuan, Fushun

Abstr. Appl. Anal. 2013, Article ID 926971, 10 p. (2013).

Summary: This paper investigates the problem of global finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. By using backstepping recursive technique and the homogeneous domination approach, a constructive design procedure for output feedback control is given. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

MSC:

93D15	Stabilization of systems by feedback
93C41	Control/observation systems with incomplete information
70F25	Nonholonomic systems related to the dynamics of a system of particles
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

finite-time output feedback stabilization; uncertain nonholonomic systems

References:

[1]	Brockett, R. W.; Brockett, R. W.; Millman, R. S.; Sussmann, H. J., Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, 2961-2963 (1983)
[2]	Astolfi, A., Discontinuous control of nonholonomic systems, Systems & Control Letters, 27, 1, 37-45 (1996) · Zbl 0877.93107
[3]	Xu, W. L.; Huo, W., Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator, Systems & Control Letters, 41, 4, 225-235 (2000) · Zbl 0980.93067
[4]	Murray, R. M.; Sastry, S. S., Nonholonomic motion planning: steering using sinusoids, IEEE Transactions on Automatic Control, 38, 5, 700-716 (1993) · Zbl 0800.93840
[5]	Jiang, Z.-P., Iterative design of time-varying stabilizers for multi-input systems in chained form, Systems & Control Letters, 28, 5, 255-262 (1996) · Zbl 0866.93084
[6]	Tian, Y.-P.; Li, S., Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control, Automatica, 38, 7, 1139-1146 (2002) · Zbl 1003.93039
[7]	Walsh, G. C.; Bushnell, L. G., Stabilization of multiple input chained form control systems, Systems & Control Letters, 25, 3, 227-234 (1995) · Zbl 0877.93100
[8]	Hespanha, J. P.; Liberzon, D.; Morse, A. S., Towards the supervisory control of uncertain nonholonomic systems, Proceedings of the American Control Conference (ACC ’99)
[9]	Liang, Z.-Y.; Wang, C.-L., Robust stabilization of nonholonomic chained form systems with uncertainties, Acta Automatica Sinica, 37, 2, 129-142 (2011) · Zbl 1240.70015
[10]	Jiang, Z.-P., Robust exponential regulation of nonholonomic systems with uncertainties, Automatica, 36, 2, 189-209 (2000) · Zbl 0952.93057
[11]	Ge, S. S.; Wang, Z.; Lee, T. H., Adaptive stabilization of uncertain nonholonomic systems by state and output feedback, Automatica, 39, 8, 1451-1460 (2003) · Zbl 1038.93079
[12]	Liu, Y.-G.; Zhang, J.-F., Output-feedback adaptive stabilization control design for non-holonomic systems with strong non-linear drifts, International Journal of Control, 78, 7, 474-490 (2005) · Zbl 1115.93082
[13]	Xi, Z.; Feng, G.; Jiang, Z. P.; Cheng, D., Output feedback exponential stabilization of uncertain chained systems, Journal of the Franklin Institute, 344, 1, 36-57 (2007) · Zbl 1119.93057
[14]	Zheng, X.; Wu, Y., Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts, Nonlinear Analysis: Theory, Methods & Applications, 70, 2, 904-920 (2009) · Zbl 1152.93048
[15]	Ju, G.; Wu, Y.; Sun, W., Output-feedback control for nonholonomic systems with linear growth condition, Journal of Systems Science & Complexity, 24, 5, 862-874 (2011) · Zbl 1269.93082
[16]	Zhao, Y.; Wu, Y. Q., Control of nonholonomic systems with nonlinear unmeasured dynamics by output feedback, Journal of Control Theory and Applications, 11, 3, 504-512 (2013)
[17]	Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, 38, 3, 751-766 (2000) · Zbl 0945.34039
[18]	Hong, Y., Finite-time stabilization and stabilizability of a class of controllable systems, Systems & Control Letters, 46, 4, 231-236 (2002) · Zbl 0994.93049
[19]	Hong, Y.; Huang, J.; Xu, Y., On an output feedback finite-time stabilization problem, IEEE Transactions on Automatic Control, 46, 2, 305-309 (2001) · Zbl 0992.93075
[20]	Huang, X.; Lin, W.; Yang, B., Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 41, 5, 881-888 (2005) · Zbl 1098.93032
[21]	Hong, Y.; Wang, J.; Cheng, D., Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE Transactions on Automatic Control, 51, 5, 858-862 (2006) · Zbl 1366.93290
[22]	Li, J.; Qian, C., Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems, IEEE Transactions on Automatic Control, 51, 5, 879-884 (2006) · Zbl 1366.93507
[23]	Li, J.; Qian, C.; Ding, S., Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems, International Journal of Control, 83, 11, 2241-2252 (2010) · Zbl 1210.93064
[24]	Shen, Y.; Huang, Y., Global finite-time stabilisation for a class of nonlinear systems, International Journal of Systems Science, 43, 1, 73-78 (2012) · Zbl 1259.93098
[25]	Zhai, J. Y., Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems, International Journal of Systems Science, 45, 3, 637-646 (2012) · Zbl 1307.93334
[26]	Hong, Y.; Wang, J.; Xi, Z., Stabilization of uncertain chained form systems within finite settling time, IEEE Transactions on Automatic Control, 50, 9, 1379-1384 (2005) · Zbl 1365.93444
[27]	Wang, J.; Zhang, G.; Li, H., Adaptive control of uncertain nonholonomic systems in finite time, Kybernetika, 45, 5, 809-824 (2009) · Zbl 1190.93086
[28]	Gao, F.; Shang, Y.; Yuan, F., Robust adaptive finite-time stabilization of nonlinearly parameterized nonholonomic systems, Acta Applicandae Mathematicae, 123, 1, 157-173 (2013) · Zbl 1255.93123
[29]	Hermes, H., Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, Differential Equations, 127, 249-260 (1991), New York, NY, USA: Dekker, New York, NY, USA
[30]	Bacciotti, A.; Rosier, L., Liapunov Functions and Stability in Control Theory (2005), Berlin, Germany: Springer, Berlin, Germany · Zbl 1078.93002
[31]	Polendo, J.; Qian, C., A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback, International Journal of Robust and Nonlinear Control, 17, 7, 605-629 (2007) · Zbl 1113.93087
[32]	Qian, C.; Lin, W., A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 46, 7, 1061-1079 (2001) · Zbl 1012.93053
[33]	Polendo, J.; Qian, C., A generalized framework for global output feedback stabilization of genuinely nonlinear systems, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC ’05)
[34]	Qian, C., A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems, Proceedings of the American Control Conference (ACC ’5)
[35]	Kurzweil, J., On the inversion of Lyapunov’s second theorem on the stability of motion, Annals of Mathematical Society Translations, 24, 2, 19-77 (1956)
[36]	Morin, P.; Pomet, J. B.; Samson, C., Developments in time varying feedback stabilization of nonlinear systems, Preprints of Nonlinear Control Systems Design Symposium, 587-594 (1998), Enschede, The Netherlands