Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay

This paper considers the stabilisation control problem of upper-triangular nonlinear time-delay systems. One distinct characteristic of this work is that the systems contain unmodelled dynamics, unknown control coefficients and time-varying delay, which make the control design much more difficult. By modifying the homogeneous domination approach and introducing a gain-scaling method, a new controller is constructed such that all the states of the closed-loop systems are bounded and convergent to the origin. Simulation examples are given to illustrate the validity of the theory.

[1]  Bahram Karimi,et al.  Decentralized Adaptive Control of Large-Scale Non-affine Nonlinear Time-Delay Systems Using Neural Networks , 2018 .

[2]  Pedro Albertos,et al.  Predictor-Based Control of a Class of Time-Delay Systems and Its Application to Quadrotors , 2017, IEEE Transactions on Industrial Electronics.

[3]  Jeen-Shing Wang,et al.  Self-adaptive recurrent neuro-fuzzy control of an autonomous underwater vehicle , 2002, IEEE Trans. Robotics Autom..

[4]  Zhen-Guo Liu,et al.  Universal strategies to explicit adaptive control of nonlinear time-delay systems with different structures , 2018, Autom..

[5]  Ranran Li.  Global output regulation of a class of lower triangular nonlinear systems with unknown control direction via output feedback , 2016, Int. J. Syst. Sci..

[6]  Yan Lin,et al.  A New Approach to Global Asymptotic Tracking for a Class of Low-Triangular Nonlinear Systems via Output Feedback , 2012, IEEE Transactions on Automatic Control.

[7]  Shihua Li,et al.  Attitude Synchronization for Flexible Spacecraft With Communication Delays , 2016, IEEE Transactions on Automatic Control.

[8]  Wei Lin,et al.  Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback , 2004, IEEE Trans. Autom. Control..

[9]  Wei Xing Zheng,et al.  Global stabilisation of a class of generalised cascaded systems by homogeneous method , 2016, Int. J. Control.

[10]  P. Kokotovic,et al.  Adaptive nonlinear design with controller-identifier separation and swapping , 1995, IEEE Trans. Autom. Control..

[11]  Kemei Zhang,et al.  A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system , 2015, Autom..

[12]  Mohamed Hamdy,et al.  Time-Varying Delay Compensation for a Class of Nonlinear Control Systems Over Network via $H_{\infty }$ Adaptive Fuzzy Controller , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Alessandro Astolfi,et al.  Nonlinear and adaptive control with applications , 2008 .

[14]  Jong-Tae Lim,et al.  Global Regulation of a Class of Uncertain Nonlinear Systems by Switching Adaptive Controller , 2010, IEEE Transactions on Automatic Control.

[15]  Zong-Yao Sun,et al.  New results on global stabilization for time‐delay nonlinear systems with low‐order and high‐order growth conditions , 2015 .

[16]  Fangzheng Gao,et al.  Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback. , 2015, ISA transactions.

[17]  Jong-Tae Lim,et al.  On global stabilization of a class of nonlinear systems with high-order nonlinearities by state feedback , 2010 .

[18]  Yuqiang Wu,et al.  Robust adaptive antiswing control of underactuated crane systems with two parallel payloads and rail length constraint. , 2016, ISA transactions.

[19]  Fangzheng Gao,et al.  Global state feedback stabilisation for a class of more general high-order non-linear systems , 2014 .

[20]  Arie Levant,et al.  Simple homogeneous sliding-mode controller , 2016, Autom..

[21]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[22]  Yisheng Zhong,et al.  Semi-global robust output tracking for non-linear uncertain systems in strict-feedback form , 2012 .

[23]  Yuqiang Wu,et al.  A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems , 2015 .

[24]  Fangzheng Gao,et al.  Further results on global state feedback stabilization of high-order nonlinear systems with time-varying delays. , 2015, ISA transactions.

[25]  Xudong Ye,et al.  Universal stabilization of feedforward nonlinear systems , 2003, Autom..

[26]  Jeen-Shing Wang,et al.  Self-adaptive recurrent neuro-fuzzy control for an autonomous underwater vehicle , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[27]  Ye Xudong,et al.  Brief Universal stabilization of feedforward nonlinear systems , 2003 .

[28]  Qingling Zhang,et al.  Adaptive Fuzzy Fault-Tolerant Tracking Control of Uncertain Nonlinear Time-Varying Delay Systems , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[29]  P. Olver.  Nonlinear Systems , 2013 .

[30]  Liang Liu,et al.  Output feedback stabilization for stochastic high-order nonlinear systems with SISS-like inverse dynamic , 2015, J. Frankl. Inst..

[31]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[32]  C. Qian,et al.  A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback , 2007 .

[33]  Yuqiang Wu,et al.  Switching-based asymptotic stabilisation of underactuated ships with non-diagonal terms in their system matrices , 2015 .

[34]  Xinghuo Yu,et al.  Chattering-free discrete-time sliding mode control , 2016, Autom..