Finite‐time tracking control of uncertain nonholonomic systems by state and output feedback

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.

[1]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[2]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[3]  Zhong-Ping Jiang,et al.  A recursive technique for tracking control of nonholonomic systems in chained form , 1999, IEEE Trans. Autom. Control..

[4]  H. Nijmeijer,et al.  Output feedback tracking of nonholonomic systems in chained form , 1999, 1999 European Control Conference (ECC).

[5]  João Pedro Hespanha,et al.  Stabilization of nonholonomic integrators via logic-based switching , 1999, Autom..

[6]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[7]  Weiliang Xu,et al.  Variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator , 2000 .

[8]  Zhong-Ping Jiang,et al.  Saturated stabilization and tracking of a nonholonomic mobile robot , 2001 .

[9]  Yu-Ping Tian,et al.  Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control , 2002, Autom..

[10]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[11]  Shuzhi Sam Ge,et al.  Adaptive stabilization of uncertain nonholonomic systems by state and output feedback , 2003, Autom..

[12]  Wilfrid Perruquetti,et al.  Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems , 2003, Autom..

[13]  E. Moulay,et al.  Finite time stability of nonlinear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[15]  Bin Wang,et al.  Finite-time tracking controller design for nonholonomic systems with extended chained form , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Wilfrid Perruquetti,et al.  Finite time stability of differential inclusions , 2005, IMA J. Math. Control. Inf..

[17]  Yiguang Hong,et al.  Stabilization of uncertain chained form systems within finite settling time , 2005, IEEE Transactions on Automatic Control.

[18]  Zhong-Ping Jiang,et al.  Output feedback exponential stabilization of uncertain chained systems , 2007, J. Frankl. Inst..

[19]  Zhao Wang,et al.  Finite-Time Tracking Control of a Nonholonomic Mobile Robot , 2008 .

[20]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[21]  Ke-cai Cao.  Global κ-exponential Tracking Control of Nonholonomic Systems in Chained-form by Output Feedback , 2009 .

[22]  Xiuyun Zheng,et al.  Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts , 2009 .

[23]  Ji Li,et al.  Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems , 2010, Int. J. Control.

[24]  Chao-Li Wang,et al.  Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties , 2011 .

[25]  Shihua Li,et al.  Finite-time tracking control of multiple nonholonomic mobile robots , 2012, J. Frankl. Inst..

[26]  F. Yuan,et al.  Robust Adaptive Finite-Time Stabilization of Nonlinearly Parameterized Nonholonomic Systems , 2013 .

[27]  Jun Fu,et al.  Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping , 2013, Autom..

[28]  Xinghuo Yu,et al.  Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances , 2013, Autom..

[29]  Yan Zhao,et al.  Global asymptotic stability controller of uncertain nonholonomic systems , 2013, J. Frankl. Inst..

[30]  Zhong-Ping Jiang,et al.  Adaptive output feedback tracking control of a nonholonomic mobile robot , 2014, Autom..

[31]  Na Xiao,et al.  Global Tracking Controller for Underactuated Ship via Switching Design , 2014 .

[32]  Yangming Zhang,et al.  Finite-time cascaded tracking control approach for mobile robots , 2014, Inf. Sci..

[33]  Shihua Li,et al.  Finite‐time formation control of multiple nonholonomic mobile robots , 2014 .

[34]  Fangzheng Gao,et al.  Finite-time state-feedback stabilisation of non-holonomic systems with low-order non-linearities , 2015 .

[35]  Xinghuo Yu,et al.  Continuous Finite-Time Output Regulation for Disturbed Systems Under Mismatching Condition , 2015, IEEE Transactions on Automatic Control.

[36]  Fangzheng Gao,et al.  Saturated finite-time stabilization of uncertain nonholonomic systems in feedforward-like form and its application , 2016 .

[37]  R. K. Barai,et al.  Design and implementation of a block‐backstepping based tracking control for nonholonomic wheeled mobile robot , 2016 .

[38]  Suiyang Khoo,et al.  Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements , 2016, Int. J. Control.

[39]  Chun-Yi Su,et al.  Vision-Based Model Predictive Control for Steering of a Nonholonomic Mobile Robot , 2016, IEEE Transactions on Control Systems Technology.

[40]  Peng Shi,et al.  Nonlinear Control for Tracking and Obstacle Avoidance of a Wheeled Mobile Robot With Nonholonomic Constraint , 2016, IEEE Transactions on Control Systems Technology.