Fixed-time stabilization of high-order linear systems: Sliding mode control scheme

A fixed-time sliding mode control scheme is designed in this paper for the high-order linear systems in the pure-feedback form with system uncertainties. A recursive procedure is utilized where a set of switching manifolds have been resorted to realize the fixed-time stability. The initial conditions of the system variables are confined in a particular region so as to avoid the singularity problem. Finally, simulation results are included to show the effectiveness of the proposed methodology established in this paper.

[1]  Masayoshi Tomizuka,et al.  Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems , 1996, IEEE Trans. Autom. Control..

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

[3]  Leonid M. Fridman,et al.  Uniform sliding mode controllers and uniform sliding surfaces , 2012, IMA J. Math. Control. Inf..

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

[5]  Z. Zuo,et al.  Non-singular fixed-time terminal sliding mode control of non-linear systems , 2015 .

[6]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[7]  Zhihong Man,et al.  Multi-input uncertain linear systems with terminal sliding-mode control , 1998, Autom..

[8]  Hong Ren Wu,et al.  A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators , 1994, IEEE Trans. Autom. Control..

[9]  Zongyu Zuo,et al.  Distributed robust finite-time nonlinear consensus protocols for multi-agent systems , 2016, Int. J. Syst. Sci..

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

[11]  Xinghuo Yu,et al.  Terminal sliding mode control design for uncertain dynamic systems , 1998 .

[12]  Jong-Hwan Kim,et al.  Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots , 1999, IEEE Trans. Robotics Autom..

[13]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[14]  Ionel Vechiu,et al.  Second-order sliding-mode controller design and tuning for grid synchronisation and power control of a wind turbine-driven doubly fed induction generator , 2013 .

[15]  Xinghuo Yu,et al.  Model reference adaptive control systems with terminal sliding modes , 1996 .

[16]  Xinghuo Yu,et al.  On nonsingular terminal sliding-mode control of nonlinear systems , 2013, Autom..

[17]  Leonid M. Fridman,et al.  Uniform Robust Exact Differentiator , 2011, IEEE Trans. Autom. Control..

[18]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[19]  Sergey Parsegov,et al.  Fixed-time consensus algorithm for multi-agent systems with integrator dynamics , 2013 .

[20]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .