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Robust stabilization of extended nonholonomic chained-form systems with dynamic nonlinear uncertain terms by using active disturbance rejection control. (English) Zbl 1421.93124

Summary: In this paper, the stabilization problem of nonholonomic chained-form systems is addressed with uncertain constants. In this paper, the active disturbance rejection control (ADRC) is designed to solve this problem. The proposed control strategy combines extended state observer (ESO) and adaptive sliding mode controller. The control of nonholonomic chained-form systems with dynamic nonlinear uncertain terms and uncertain constants is first discussed in this paper. In comparison with existing methods, the proposed method in this paper has better performance. It is proved that, with the application of the proposed control strategy, semiglobal finite-time stabilization of the systems is achieved. An example is given to illustrate the effectiveness of the proposed method.

MSC:

93D21 Adaptive or robust stabilization
93C20 Control/observation systems governed by partial differential equations
93C40 Adaptive control/observation systems
93B12 Variable structure systems
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[1] 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 · doi:10.1109/9.277235
[2] Wang, Q.; Ran, M.; Dong, C., On finite-time stabilization of active disturbance rejection control for uncertain nonlinear systems, Asian Journal of Control, 20, 1, 415-424 (2018) · Zbl 1391.93189 · doi:10.1002/asjc.1558
[3] Butt, Y. A., Robust stabilization of a class of nonholonomic systems using logical switching and integral sliding mode control, Alexandria Engineering Journal, 57, 3, 1591-1596 (2018)
[4] Wang, H.; Zhu, Q., Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization, Automatica, 98, 247-255 (2018) · Zbl 1406.93269 · doi:10.1016/j.automatica.2018.09.026
[5] Gao, F.; Wu, Y.; Li, H.; Liu, Y., Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application, International Journal of Systems Science, 49, 10, 2155-2169 (2018) · Zbl 1482.93546 · doi:10.1080/00207721.2018.1494863
[6] Shi, S.; Xu, S.; Yu, X.; Li, Y.; Zhang, Z., Finite-time tracking control of uncertain nonholonomic systems by state and output feedback, International Journal of Robust and Nonlinear Control, 28, 6, 1942-1959 (2018) · Zbl 1390.93332 · doi:10.1002/rnc.3991
[7] Brockett, R. W., Asymptotic Stability and Feedback Stabilization in Differential Geometric Control Theory (1983), Berlin, Germany: Springer, Berlin, Germany · Zbl 0528.93051
[8] Sun, W., Adaptive sliding-mode tracking control for a class of nonholonomic mechanical systems, Mathematical Problems in Engineering, 2013 (2013) · Zbl 1299.93202 · doi:10.1155/2013/734307
[9] Gao, F.; Yuan, F., Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems, ISA Transactions, 54, 75-82 (2015) · doi:10.1016/j.isatra.2014.07.009
[10] Butt, Y. A., Robust stabilization of a class of nonholonomic systems using logical switching and integral sliding mode control, Alexandria Engineering Journal, 57, 3, 1591-1596 (2017)
[11] Zhu, C.; Li, C.; Zhang, K.; Wei, H., Fault tolerant control for a general class of nonholonomic dynamic systems via terminal sliding mode, Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
[12] Pomet, J.-B.; Thuilot, B.; Bastin, G.; Campion, G., A hybrid strategy for the feedback stabilization of nonholonomic mobile robots, Proceedings of the 1992 IEEE International Conference on Robotics and Automation
[13] Astolfi, A., Discontinuous control of nonholonomic systems, Systems & Control Letters, 27, 1, 37-45 (1996) · Zbl 0877.93107 · doi:10.1016/0167-6911(95)00041-0
[14] Tian, Y.; Li, S., Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control, Automatica, 38, 7, 1139-1146 (2002) · Zbl 1003.93039 · doi:10.1016/S0005-1098(01)00303-X
[15] Jiang, T.; Huang, C.; Guo, L., Control of uncertain nonlinear systems based on observers and estimators, Automatica, 59, 35-47 (2015) · Zbl 1326.93073 · doi:10.1016/j.automatica.2015.06.012
[16] Mobayen, S.; Javadi, S., Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode, Journal of Vibration and Control, 23, 2, 181-189 (2015) · doi:10.1177/1077546315576611
[17] Mobayen, S., Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method, Nonlinear Dynamics, 80, 1-2, 669-683 (2015) · Zbl 1345.93141 · doi:10.1007/s11071-015-1897-4
[18] Chen, H.; Wang, C.; Liang, Z.; Zhang, D.; Zhang, H., Robust practical stabilization of nonholonomic mobile robots based on visual servoing feedback with inputs saturation, Asian Journal of Control, 16, 3, 692-702 (2014) · Zbl 1302.93186 · doi:10.1002/asjc.829
[19] Chen, H.; Shihong, D.; Chen, X., Global finite-time stabilization for nonholonomic mobile robots based on visual servoing, International Journal of Advanced Robotic Systems (2014)
[20] Ding, S.; Zheng, W. X.; Sun, J.; Wang, J., Second-order sliding-mode controller design and its implementation for buck converters, IEEE Transactions on Industrial Informatics, 14, 5, 1990-2000 (2018) · doi:10.1109/TII.2017.2758263
[21] Roozegar, M.; Mahjoob, M. J.; Ayati, M., Adaptive tracking control of a nonholonomic pendulum-driven spherical robot by using a model-reference adaptive system, Journal of Mechanical Science and Technology, 32, 2, 845-853 (2018) · doi:10.1007/s12206-018-0135-z
[22] Sarfraz, M.; Rehman, F.-U., Feedback stabilization of nonholonomic drift-free systems using adaptive integral sliding mode control, Arabian Journal for Science and Engineering, 42, 7, 2787-2797 (2017) · doi:10.1007/s13369-017-2436-z
[23] Gao, F. Z.; Yuan, F. S.; Yao, H. J., Robust adaptive control for nonholonomic systems with nonlinear parameterization, Nonlinear Analysis: Real World Applications, 11, 4, 3242-3250 (2010) · Zbl 1214.93038 · doi:10.1016/j.nonrwa.2009.11.019
[24] Yuan, H.; Qu, Z., Continuous time-varying pure feedback control for chained nonholonomic systems with exponential convergent rate, IFAC Proceedings Volumes, 41, 2, 15203-15208 (2008) · doi:10.3182/20080706-5-KR-1001.02571
[25] Tian, Y.-P.; Cao, K.-C., Time-varying linear controllers for exponential tracking of non-holonomic systems in chained form, International Journal of Robust and Nonlinear Control, 17, 7, 631-647 (2007) · Zbl 1113.93058 · doi:10.1002/rnc.1149
[26] Jiang, Z. P.; Pomet, J.-B., Global stabilization of parametric chained-form systems by time-varying dynamic feedback, International Journal of Adaptive Control and Signal Processing, 10, 1, 47-59 (1996) · Zbl 0866.93093 · doi:10.1002/(SICI)1099-1115(199601)10:1<47::AID-ACS385>3.0.CO;2-7
[27] Ding, S.; Qian, C.; Li, S.; Li, Q., Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations, International Journal of Robust and Nonlinear Control, 21, 3, 271-294 (2011) · Zbl 1213.93182 · doi:10.1002/rnc.1591
[28] Ding, S.; Zheng, W. X., Nonsingular terminal sliding mode control of nonlinear second-order systems with input saturation, International Journal of Robust and Nonlinear Control, 26, 9, 1857-1872 (2016) · Zbl 1342.93034 · doi:10.1002/rnc.3381
[29] Ding, S.; Zheng, W. X., Robust control of multiple integrators subject to input saturation and disturbance, International Journal of Control, 88, 4, 844-856 (2015) · Zbl 1316.93100 · doi:10.1080/00207179.2014.982710
[30] Pan, H. H.; Sun, W. C.; Gao, H. J.; Yu, J. Y., Finite-time stabilization for vehicle active suspension systems with hard constraints, IEEE Transactions on Intelligent Transportation Systems, 16, 5, 2663-2672 (2015) · doi:10.1109/tits.2015.2414657
[31] Pan, H.; Sun, W., Nonlinear output feedback finite-time control for vehicle active suspension systems, IEEE Transactions on Industrial Informatics (2018) · doi:10.1109/TII.2018.2866518
[32] Gao, F. Z.; Shang, Y. L.; Yuan, F. S., Robust adaptive finite-time stabilization of nonlinearly parameterized nonholonomic systems, Acta Applicandae Mathematicae, 123, 1, 157-173 (2013) · Zbl 1255.93123 · doi:10.1007/s10440-012-9759-2
[33] Gao, F. Z.; Yuan, F. S.; Yao, H. J.; Mu, X. W., Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts, Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, 35, 9, 4222-4233 (2011) · Zbl 1225.93093 · doi:10.1016/j.apm.2011.02.042
[34] Chen, H.; Zhang, B.; Zhao, T.; Wang, T.; Li, K., Finite-time tracking control for extended nonholonomic chained-form systems with parametric uncertainty and external disturbance, Journal of Vibration and Control, 24, 1, 100-109 (2018) · Zbl 1381.93051 · doi:10.1177/1077546316633568
[35] Yang, F.; Wang, C.-L., Adaptive stabilization for uncertain nonholonomic dynamic mobile robots based on visual servoing feedback, Zidonghua Xuebao/Acta Automatica Sinica, 37, 7, 857-864 (2011) · Zbl 1265.68295 · doi:10.1016/S1874-1029(11)60211-5
[36] Chen, H.; Zhang, J., Global practical stabilization for non-holonomic mobile robots with uncalibrated visual parameters by using a switching controller, IMA Journal of Mathematical Control and Information, 30, 4, 543-557 (2013) · Zbl 1279.93076 · doi:10.1093/imamci/dns044
[37] Han, J. Q., A class of extended state observers for uncertain systems, Control and Decision, 10, 1, 85-88 (1995)
[38] Guo, B.-Z.; Zhao, Z.-L., On the convergence of an extended state observer for nonlinear systems with uncertainty, Systems & Control Letters, 60, 6, 420-430 (2011) · Zbl 1225.93056 · doi:10.1016/j.sysconle.2011.03.008
[39] Guo, B.; Zhao, Z., On convergence of the nonlinear active disturbance rejection control for MIMO systems, SIAM Journal on Control and Optimization, 51, 2, 1727-1757 (2013) · Zbl 1266.93075 · doi:10.1137/110856824
[40] Freidovich, L. B.; Khalil, H. K., Performance recovery of feedback-linearization-based designs, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 53, 10, 2324-2334 (2008) · Zbl 1367.93498 · doi:10.1109/TAC.2008.2006821
[41] Zhao, Z.-L.; Guo, B.-Z., On active disturbance rejection control for nonlinear systems using time-varying gain, European Journal of Control, 23, 62-70 (2015) · Zbl 1360.93212 · doi:10.1016/j.ejcon.2015.02.002
[42] Bhat, S. P.; Bernstein, D. S., Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals, and Systems, 17, 2, 101-127 (2005) · Zbl 1110.34033 · doi:10.1007/s00498-005-0151-x
[43] Yu, S.; Yu, X.; Shirinzadeh, B.; Man, Z., Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 41, 11, 1957-1964 (2005) · Zbl 1125.93423 · doi:10.1016/j.automatica.2005.07.001
[44] Shtessel, Y.; Edwards, C.; Fridman, L.; Levant, A., Sliding mode control and observation, International Journal of Control, 9, 213-249 (2014)
[45] Nazrulla, S.; Khalil, H. K., Robust stabilization of non-minimum phase nonlinear systems using extended high-gain observers, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 56, 4, 802-813 (2011) · Zbl 1368.93631 · doi:10.1109/TAC.2010.2069612
[46] Chen, H.; Xu, S.; Chu, L.; Tong, F.; Chen, L., Finite-time switching control of nonholonomic mobile robots for moving target tracking based on polar coordinates, Complexity, 2018 (2018) · Zbl 1407.93245 · doi:10.1155/2018/7360643
[47] Defoort, M.; Demesure, G.; Uo, Z.; Zuo, Z.; Polyakov, A.; Djemai, M., Fixed-time stabilisation and consensus of non-holonomic systems, IET Control Theory & Applications, 10, 18, 2497-2505 (2016) · doi:10.1049/iet-cta.2016.0094
[48] Zhang, Z.; Wu, Y., Fixed-time regulation control of uncertain nonholonomic systems and its applications, International Journal of Control, 90, 7, 1327-1344 (2017) · Zbl 1367.93595 · doi:10.1080/00207179.2016.1205758
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