Finite-time tracking control of uncertain nonholonomic systems by state and output feedback
Shang Shi
School of Automation, Nanjing University of Science and Technology, Nanjing, China
Search for more papers by this authorCorresponding Author
Shengyuan Xu
School of Automation, Nanjing University of Science and Technology, Nanjing, China
Correspondence
Shengyuan Xu, School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China.
Email: [email protected]
Search for more papers by this authorXin Yu
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China
Search for more papers by this authorYongmin Li
School of Science, Huzhou Teachers College, Huzhou, China
Search for more papers by this authorZhengqiang Zhang
School of Electrical Engineering and Automation, Qufu Normal University, Rizhao, China
Search for more papers by this authorShang Shi
School of Automation, Nanjing University of Science and Technology, Nanjing, China
Search for more papers by this authorCorresponding Author
Shengyuan Xu
School of Automation, Nanjing University of Science and Technology, Nanjing, China
Correspondence
Shengyuan Xu, School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China.
Email: [email protected]
Search for more papers by this authorXin Yu
School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China
Search for more papers by this authorYongmin Li
School of Science, Huzhou Teachers College, Huzhou, China
Search for more papers by this authorZhengqiang Zhang
School of Electrical Engineering and Automation, Qufu Normal University, Rizhao, China
Search for more papers by this authorSummary
This paper studies the finite-time tracking control of nonholonomic systems in chained form with parameter uncertainties, unknown output gains, and mismatched uncertainties. To achieve the finite-time tracking control of uncertain nonholonomic systems, we propose 2 types of controllers by state and output feedback, respectively. Both of the proposed 2 types of controllers can achieve the finite-time output tracking control of the nonholonomic systems even in the presence of mismatched uncertainties and/or unknown gains. The effectiveness of our proposed controllers are illustrated with simulation examples.
REFERENCES
- 1Yang H, Fan X, Shi P, Hua C. Nonlinear control for tracking and obstacle avoidance of a wheeled mobile robot with nonholonomic constraint. IEEE Trans Control Syst Technol. 2016; 24(2): 741-746.
- 2Li Z, Yang C, Su CY, Deng J. Vision-based model predictive control for steering of a nonholonomic mobile robot. IEEE Trans Control Syst Technol. 2016; 24(2): 553-564.
- 3Brockett RW. Asymptotic stability and feedback stabilization. Differ Geom Control Theory. 1983; 27(1): 181-191.
- 4Xu WL, Huo W. Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator. Syst Control Lett. 2000; 41(4): 225-235.
- 5Wu Y, Zhao Y, Yu J. Global asymptotic stability controller of uncertain nonholonomic systems. J Franklin Inst. 2013; 350(5): 1248-1263.
- 6Tian YP, Li S. Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control. Automatica. 2002; 38(7): 1139-1146.
- 7Hespanha JP, Morse AS. Stabilization of nonholonomic integrators via logic-based switching. Automatica. 1999; 35(3): 385-393.
- 8Jiang ZP, Nijmeijer H. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Trans Autom Control. 1999; 44(2): 265-279.
- 9Fu J, Chai T, Su CY, Jin Y. Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping. Automatica. 2013; 49(12): 3682-3686.
- 10Ou M, Du H, Li S. Finite-time formation control of multiple nonholonomic mobile robots. Int J Robust Nonlinear Control. 2014; 24(1): 140-165.
- 11Rudra S, Barai RK, Maitra M. Design and implementation of a block-backstepping based tracking control for nonholonomic wheeled mobile robot. Int J Robust Nonlinear Control. 2016; 26(14): 3018-3035.
- 12Hong Y, Wang J, Xi Z. Stabilization of uncertain chained form systems within finite settling time. IEEE Trans Autom Control. 2005; 50(9): 1379-1384.
- 13Gao F, Shang Y, Yuan F. Robust adaptive finite-time stabilization of nonlinearly parameterized nonholonomic systems. Acta Appl Math. 2013; 123(1): 157-173.
- 14Floquet T, Barbot JP, Perruquetti W. Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems. Automatica. 2003; 39(6): 1077-1083.
- 15Wu Y, Gao F, Zhang Z. Saturated finite-time stabilization of uncertain nonholonomic systems in feedforward-like form and its application. Nonlinear Dynamics. 2016; 84(3): 1609-1622.
- 16Wu Y, Gao F, Liu Z. Finite-time state-feedback stabilization of nonholonomic systems with low-order non-linearities. IET Control Theory Appl. 2015; 9(10): 1553-1560.
- 17Liang ZY, Wang CL. Robust stabilization of nonholonomic chained form systems with uncertainties. Acta Automatica Sin. 2011; 37(2): 129-142.
- 18Zhang Y, Liu G, Luo B. Finite-time cascaded tracking control approach for mobile robots. Inform Sci. 2014; 284(284): 31-43.
- 19Wang Z, Li S, Fei S. Finite-time tracking control of a nonholonomic mobile robot. Asian J Control. 2009; 11(3): 344-357.
- 20Ou M, Du H, Li S. Finite-time tracking control of multiple nonholonomic mobile robots. J Franklin Inst. 2012; 349(9): 2834-2860.
- 21Wu Y, Zhang Z, Xiao N. Global tracking controller for underactuated ship via switching design. J Dyn Syst Meas Control. 2014; 136(9): 1-7.
- 22Wu Y, Wang B, Zong GD. Finite-time tracking controller design for nonholonomic systems with extended chained form. IEEE Trans Circuits Syst II, Exp Briefs. 2005; 52(11): 798-802.
- 23Ge SS, Wang Z, Lee TH. Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. Automatica. 2003; 39(8): 1451-1460.
- 24Xi Z, Feng G, Jiang ZP, Cheng D. Output feedback exponential stabilization of uncertain chained systems. J Franklin Inst. 2007; 344(1): 36-57.
- 25Zheng X, Wu Y. Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts. Nonlinear Anal Theory Methods Appl. 2009; 70(2): 904-920.
- 26Huang J, Wen C, Wang W, Jiang ZP. Adaptive output feedback tracking control of a nonholonomic mobile robot. Automatica. 2014; 50(3): 821-831.
- 27Lefeber E, Robertsson A, Nijmeijer H. Output feedback tracking of nonholonomic systems in chained form. Paper presented at: European Control Conference; 1999; Karlsruhe, Germany.
- 28Ke-Cai C. Global κ-exponential tracking control of nonholonomic systems in chained-form by output feedback. Acta Automatica Sin. 2009; 35(5): 568-576.
10.1016/S1874-1029(08)60087-7 Google Scholar
- 29Shi S, Yu X, Khoo S. Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements. Int J Control. 2016; 89(2): 411-423.
- 30Bhat SP, Bernstein DS. Finite-time stability of continuous autonomous systems. SIAM J Control Optim. 2000; 38(3): 751-766.
- 31Moulay E, Perruquetti W. Finite time stability of nonlinear systems. Paper Presented at: 42nd IEEE Conference on Decision and Control; 2003; Maui, HI, USA.
- 32Filippov AF. Differential Equations with Discontinuous Righthand Side. Amsterdam, The Netherlands: Kluwer Academic Publishers; 1988.
10.1007/978-94-015-7793-9 Google Scholar
- 33Moulay E, Perruquetti W. Finite time stability of differential inclusions. IMA J Math Control Inf. 2005; 22(4): 465-475.
- 34Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge, UK: Cambridge University Press; 1952.
- 35Isidori A. Nonlinear Control Systems. London, UK: Springer-Verlag; 1995.
10.1007/978-1-84628-615-5 Google Scholar
- 36Levant A. Higher-order sliding modes, differentiation and output-feedback control. Int J Control. 2003; 76(9-10): 924-941.
- 37Yang J, Li S, Su J, Yu X. Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances. Automatica. 2013; 49(7): 2287-2291.
- 38Li S, Sun H, Yang J, Yu X. Continuous finite-time output regulation for disturbed systems under mismatching condition. IEEE Trans Autom Control. 2015; 60(1): 277-282.
- 39Huang X, Lin W, Yang B. Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica. 2005; 41(5): 881-888.
- 40Li J, Qian C, Ding S. Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. Int J Control. 2010; 83(11): 2241-2252.
- 41Jiang ZP, Lefeber E, Nijmeijer H. Saturated stabilization and tracking of a nonholonomic mobile robot. Syst Control Lett. 2001; 42(5): 327-332.
