Tracking Control of a Class of Differential Inclusion Systems via Sliding Mode Technique

The tracking problem for a class of differential inclusion systems is investigated. Using global sliding mode control approach, a tracking control is proposed such that the output of a differential inclusion system tracks the desired trajectory asymptotically. An extensive reaching law is proposed to achieve the chattering reduction. Finally, an example is given to illustrate the validity of the proposed design.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[3]  H. Yau.  Design of adaptive sliding mode controller for chaos synchronization with uncertainties , 2004 .

[4]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[5]  Jun Huang,et al.  Uniformly ultimately bounded tracking control of linear differential inclusions with stochastic disturbance , 2011, Math. Comput. Simul..

[6]  Yang Liu,et al.  Asymptotic tracking control for a class of reference signals for linear differential inclusions , 2014, Int. J. Syst. Sci..

[7]  Yeong-Jeu Sun.  Stability criteria for a class of differential inclusion systems with discrete and distributed time delays , 2009 .

[8]  Daniel W. C. Ho,et al.  Sliding mode control of switched hybrid systems with stochastic perturbation , 2011, Syst. Control. Lett..

[9]  Y. Pyatnitskiy,et al.  Criteria of asymptotic stability of differential and difference inclusions encountered in control theory , 1989 .

[10]  Jia-Wen Chen.  Asymptotic Stability for Tracking Control of Nonlinear Uncertain Dynamical Systems Described by Differential Inclusions , 2001 .

[11]  Yeong-Jeu Sun,et al.  Composite tracking control for a class of uncertain nonlinear control systems with uncertain deadzone nonlinearities , 2008 .

[12]  Xiaona Song,et al.  Sliding mode control with disturbance observer for a class of nonlinear systems , 2012, Int. J. Autom. Comput..

[13]  Tingshu Hu,et al.  Nonlinear control design for linear differential inclusions via convex hull of quadratics , 2007, Autom..

[14]  Jun Huang,et al.  Output tracking and disturbance rejection of linear differential inclusion systems , 2012, Int. J. Syst. Sci..

[15]  Aria Alasty,et al.  Chaos control in uncertain dynamical systems using nonlinear delayed feedback , 2009 .

[16]  A. B. Rad,et al.  Robust fuzzy tracking control for robotic manipulators , 2007, Simul. Model. Pract. Theory.

[17]  Chyun-Chau Fuh,et al.  A robust controller for chaotic systems under external excitation , 2002 .

[18]  Zhengzhi Han,et al.  Global sliding mode control and application in chaotic systems , 2009 .

[19]  Jamal M. Nazzal,et al.  Chaos control using sliding-mode theory , 2007 .

[20]  Xun Gong,et al.  Adaptive backstepping sliding mode trajectory tracking control for a quad-rotor , 2012, Int. J. Autom. Comput..

[21]  G. Smirnov.  Introduction to the Theory of Differential Inclusions , 2002 .

[22]  Jun Huang,et al.  Robust stabilization of linear differential inclusion system with time delay , 2010, Math. Comput. Simul..