Output-feedback control for nonholonomic systems with linear growth condition. (English) Zbl 1269.93082

Summary: This paper deals with the stabilization of the nonholonomic systems with strongly nonlinear uncertainties. The objective is to design an output feedback law such that the closed-loop system is globally asymptotically regulated at the origin. The systematic strategy combines the input-state scaling technique with the backstepping technique. A novel switching control strategy based on the output measurement of the first subsystem is employed to make the subsystem far away from the origin. The simulation demonstrates the effectiveness of the proposed controller.


93D15 Stabilization of systems by feedback
93B52 Feedback control
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI


[1] C. C. Wit and O. J. Sordalen, Expunential stabilization of mobile robots with nonholonomic constraints, IEEE Trans. Automat. Control, 1992, 37(11): 1791–1797. · Zbl 0778.93077 · doi:10.1109/9.173153
[2] R. Mccolockey and R. Murray, Exponential stabilization of driftless nonlinear control systems using homogeneous feedback, IEEE Trans. Automat. Control, 1997, 42(5): 614–628. · Zbl 0882.93066 · doi:10.1109/9.580865
[3] R. Murray and S. Sastry, Nonholonomic motion planning steering using sinusoids, IEEE Trans. Automat. Control, 1993, 38(5): 700–716. · Zbl 0800.93840 · doi:10.1109/9.277235
[4] Z. D. Sun, S. S. Ge, W. Huo, et al., Stabilization of nonholonomic chained systems via nonregular feedback linerization, Systems and Control Letters, 2001, 44(4): 279–289. · Zbl 0986.93016 · doi:10.1016/S0167-6911(01)00148-7
[5] W. Brockett, Asymptotic Stability and Feedback Stabilization, R. W. Brockett, R. S. Millman, H.J. Sussman (Eds.), Differential Geometric Control Theory, 1983. · Zbl 0528.93051
[6] A. Astolfi, Discontiouous control of nonholonomic systems, Systems and Control Letters, 1996, 27(1): 37–45. · Zbl 0877.93107 · doi:10.1016/0167-6911(95)00041-0
[7] G. C. Walsh and L. G. Bushnell, Stabilization of multiple input chained form control systems, Systems and Control Letters, 1995, 26(3): 227–234. · Zbl 0877.93100 · doi:10.1016/0167-6911(94)00061-Y
[8] Y. P. Tian and S. H. Li, Exponential stabilization of nonholonomic systems by smooth time varying control, Automatica, 2002, 38(7): 1139–1146. · Zbl 1003.93039 · doi:10.1016/S0005-1098(01)00303-X
[9] O. J. Sordalen and C. C. Wit, Exponential stabilization of nonholonomic chained systems, IEEE Trans. Automat. Control, 1995, 40(1): 35–49. · Zbl 0828.93055 · doi:10.1109/9.362901
[10] Z. Xi, G. Feng, Z. P. Jiang, et al., A switching algorithm for global exponential stabilization of uncertain chained systems, IEEE Trans. Automat. Control, 2003, 48(10): 1793–1798. · Zbl 1364.93674 · doi:10.1109/TAC.2003.817937
[11] Y. G. Liu and J. F. Zhang, Output-feedback adaptive stabilization control design for nonholonomic systems with strong nonlinear drifts, International Journal of Control, 2005, 78(7): 474–490. · Zbl 1115.93082 · doi:10.1080/00207170500080280
[12] Q. D. Wang, C. L. Wei, and S. Y. Zhang, The output feedback control for uncertain nonholonomic systems with uncertainties, Journal of Control Theorey and Application, 2006, 23(2): 128–132. · Zbl 1303.93089 · doi:10.1007/s11768-006-4245-x
[13] S. S. Ge, Z. P. Wang, and T. H. Lee, Adaptive stabilization of uncertain nonholonomic systems by atate and output feedback, Automatica, 2003, 39(8): 1451–1460. · Zbl 1038.93079 · doi:10.1016/S0005-1098(03)00119-5
[14] Z. P. Jiang and H. Nijmeijer, A recursive technique for tracking control of nonholonomic systems in chained form, IEEE Trans. Automat. Control, 1999, 44(2): 265–279. · Zbl 0978.93046 · doi:10.1109/9.746253
[15] Z. Xi, G. Feng, Z. P. Jiang, et al., Output feedback exponential stabilization of uncertain chained systems, Journal of Franklin Institute, 2007, 344(1): 36–57. · Zbl 1119.93057 · doi:10.1016/j.jfranklin.2005.10.002
[16] K. D. Do and J. Pan, Adaptive global stabilization of nonholonomic systems with strong nonlinear drifts, Systems and Control Letters, 2002, 46(3): 195–205. · Zbl 0994.93055 · doi:10.1016/S0167-6911(02)00133-0
[17] Z. P. Jiang, Iterative design of time-varying stabilizers for multi-input systems in chained form, Systems and Control Letters, 1996, 28(5): 255–262. · Zbl 0866.93084 · doi:10.1016/0167-6911(96)00029-1
[18] C. Qian and W. Lin, Output feedback control of a class of nonlinear systems: A nonseparation principle paredigm, IEEE Trans. Automat. Control, 2002, 47(10): 1710–1715. · Zbl 1364.93720 · doi:10.1109/TAC.2002.803542
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