Nonsingular Global Fixed-Time Stabilization for Nonlinear Systems

Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. *e results of simulations verify the effectiveness of the proposed method.

[1]  J. Back,et al.  Nonsmooth feedback stabilizer for strict-feedback nonlinear systems that may not be linearizable at the origin , 2007, Syst. Control. Lett..

[2]  Jun Fu,et al.  Adaptive Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems via Logic-Based Switchings , 2017, IEEE Transactions on Automatic Control.

[3]  Xin-Ping Guan,et al.  Finite/Fixed-Time Stabilization for Nonlinear Interconnected Systems With Dead-Zone Input , 2017, IEEE Transactions on Automatic Control.

[4]  Yu Zhao,et al.  Appointed-time consensus: Accurate and practical designs , 2018, Autom..

[5]  Arie Levant,et al.  Accelerated Twisting Algorithm , 2015, IEEE Transactions on Automatic Control.

[6]  Xinghuo Yu,et al.  Fixed-time converging terminal surface with non-singular control design for second-order systems , 2017 .

[7]  Xiaoxiao Lu,et al.  Fixed-time control of delayed neural networks with impulsive perturbations , 2018, Nonlinear Analysis: Modelling and Control.

[8]  Andrey Polyakov,et al.  Finite-time and fixed-time stabilization: Implicit Lyapunov function approach , 2015, Autom..

[9]  Dan Yang,et al.  Finite-Time Stability for a Class of Underactuated Systems Subject to Time-Varying Disturbance , 2020, Complex..

[10]  Hong Wang,et al.  A fixed-time output feedback control scheme for double integrator systems , 2017, Autom..

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

[12]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[13]  Ting Li,et al.  A new approach to fast global finite-time stabilization of high-order nonlinear system , 2017, Autom..

[14]  Yuanwei Jing,et al.  Adaptive output tracking control of a class of nonlinear systems , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[15]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[16]  Yongduan Song,et al.  Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time , 2017, Autom..