Sliding mode control via system immersion and application in chaos control

This paper focuses on the stabilization of nonlinear systems using sliding mode control (SMC). Motivated by a newly proposed stabilization approach named system immersion and manifold invariance (I&I), a systemic design method is proposed to design the sliding surface. As well as the I&I stabilization approach, SMC method based on system immersion is applied to chaos control in the Lorenz chaotic system, and simulation results are provided to validate the proposed schemes.

[1]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

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

[3]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[4]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[5]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[6]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[7]  Wei Zhang,et al.  Sliding mode control for chaotic systems based on LMI , 2009 .

[8]  Chun-Liang Lin,et al.  A general class of sliding surface for sliding mode control , 1998, IEEE Trans. Autom. Control..

[9]  Alessandro Astolfi,et al.  A constructive solution for stabilization via immersion and invariance: The cart and pendulum system , 2008, Autom..

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

[11]  Wei Zhang,et al.  Stabilization of center systems via immersion and invariance , 2009 .

[12]  Alessandro Astolfi,et al.  Immersion and invariance adaptive control of linear multivariable systems , 2003, Syst. Control. Lett..

[13]  Alessandro Astolfi,et al.  Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems , 2001, IEEE Trans. Autom. Control..