The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method

This paper treats the exponential stabilization of a class of n-D chaotic systems. A new control approach which is called the exact solution method is presented. The most important feature of this method is that the solution of the system under consideration can be carefully designed to converge exponentially to the origin. Based on this method, the exponential stabilization of a class of n-D chaotic systems and its application in controlling chaotic system with unknown parameter are presented. The Genesio-Tesi system is taken to give the numerical simulation which is completely consistent with the theoretical analysis presented in this paper.

[1]  Nooshin Bigdeli,et al.  Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems , 2017, J. Frankl. Inst..

[2]  Emad E. Mahmoud,et al.  Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control , 2017 .

[3]  Mohammad Ali Akhaee,et al.  Fast synchronization of non-identical chaotic modulation-based secure systems using a modified sliding mode controller , 2016 .

[4]  Abdelkrim Boukabou,et al.  Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model , 2014, Math. Comput. Simul..

[5]  Sameer Kumar,et al.  Synchronization of a class of chaotic systems via derivative control , 2016, 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES).

[6]  R. Luo,et al.  The stability of impulsive incommensurate fractional order chaotic systems with Caputo derivative , 2018, Chinese Journal of Physics.

[7]  V. J. Majd,et al.  Sliding mode control for uncertain new chaotic dynamical system , 2009 .

[8]  Yuming Feng,et al.  Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control , 2017, Complex..

[9]  Song Zheng,et al.  Multi-switching combination synchronization of three different chaotic systems via nonlinear control , 2016 .

[10]  Bo Wang,et al.  On the synchronization of a class of chaotic systems based on backstepping method , 2007 .

[11]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[12]  Hamed Tirandaz,et al.  On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control , 2018 .

[13]  M. Yassen.  Controlling, synchronization and tracking chaotic Liu system using active backstepping design , 2007 .

[14]  Runzi Luo,et al.  The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output , 2018, Complex..

[15]  Sara Dadras,et al.  Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach , 2009 .

[16]  S. Effati,et al.  Optimal and adaptive control for a kind of 3D chaotic and 4D hyper-chaotic systems , 2014 .